Last May 19, President Clinton and P.V. Narasimha Rao, India's prime minister, concluded talks in Washington with a formal statement that attracted little attention -- except in the office of Tom Graham, the administration's chief lobbyist for winning extension of the nuclear Non-Proliferation Treaty.

One sentence caught Graham's eye. It said the two countries "offered their strong support" for efforts to prevent the spread of nuclear weapons -- "with the goal of elimination of such weapons."

Eliminating nuclear weapons was not something that U.S. presidents talked about publicly, even in this vague way. During the Cold War, when the United States and the Soviet Union had tens of thousands of nuclear missiles aimed at each other, it was hardly worth considering. Now, though, the Cold War was over, and the NPT was coming up for renewal. Graham seized on Clinton's statement as he sought to line up votes for indefinite extension of the 25-year-old treaty.

Last summer and fall, Graham traveled to more than 40 countries on nearly every continent. In meetings with diplomats, he repeatedly cited Clinton's statement as evidence of U.S. commitment to one of the treaty's central provisions: that the world's five nuclear powers would work toward the elimination of all nuclear weapons, including their own.

Back in Washington, diplomats read Graham's cables from his travels and concluded that his assertions were out of line with U.S. policy. Senior administration officials and military leaders concurred in the view that the United States needed to keep its nuclear arsenal for the foreseeable future. What was Graham doing? they asked.

For two decades, U.S. officials had dodged questions about the contradiction between the NPT's goals and U.S. nuclear policy. Now, Graham believed, the world's nuclear balance had changed dramatically and the United States could afford to live up to the NPT pledge. It was both the right decision and good politics, he had concluded.

The wisdom of Graham's approach remains uncertain on the eve of the NPT talks, which open Monday at U.N. headquarters in New York. Delegates from more than 170 nations will gather for a month-long conference ending in a vote on the future of the NPT.

The treaty emerged in the late 1960s as a statement against instability. It divided the world's nations into nuclear haves and have-nots: The vast majority of nations pledged never to acquire nuclear weapons, while the United States, the Soviet Union (now Russia), China, Britain and France were permitted to keep their arsenals as long as they pledged to work toward total disarmament.

The U.S. government has taken the position that the NPT should be extended indefinitely and without conditions. U.S. officials argue that the NPT helps to prevent the spread of nuclear weapons and thus makes nuclear war less likely. If the NPT regime were to erode or collapse, they say, scores of new countries might be tempted to acquire nuclear bombs -- threatening not just the United States, but one another.

Scores of Third World governments -- and some wealthy countries such as Japan, Sweden and New Zealand -- see the NPT extension vote as perhaps their last chance to pressure the United States, Russia, China, Britain and France into giving up their nuclear weapons. Many are resisting an indefinite extension, fearing they will lose all their leverage. The five powers possess about 45,000 nuclear bombs; not one of them has stated unequivocally that eliminating all nuclear weapons -- the "zero option" -- is desirable or practical.

Into this morass of contradiction and debate stepped Graham, an articulate Republican diplomat with 25 years of experience in the arms control process. Graham believed deeply in the NPT's precepts; he had fought hard during internal Clinton administration debates in 1993 to change U.S. nuclear policy to help win the NPT vote. But as the son of a Democratic ward politician in Louisville, Ky., Graham also knew something about the stamina and gamesmanship necessary to prevail at a roiling political convention.

Throughout 1994, Graham hopped and skipped across the globe as if he could round up the required votes by sheer energy alone. From Rabat to Windhoek to Katmandu, he tromped into foreign ministries and preached the NPT's virtues. He emphasized the treaty's role in making small nations around the world more secure. Morocco had to worry about the possibility of Islamic revolutionaries taking over next door in Algeria. Namibia could hardly be comfortable in a world where its South African neighbors were free to pursue nuclear weapons. How would Nepal fare if South Asian nations pursued an unfettered nuclear arms race?

Yet in many of these capitals, nuclear weapons seemed to be the least of the government's problems. Some officials Graham met had barely heard of the NPT, never mind having decided how they might vote. In a sense, the NPT regime had worked so well over its 25-year life that many nations now took it for granted.

Graham's strategy partly involved rounding up as many votes as possible from smaller countries. Because all votes will count equally, little Togo wielded just as much clout as populous Nigeria.

Some of the largest and most influential nations in the developing world -- Mexico, Indonesia, Egypt, Iran and Nigeria -- were far from sympathetic to Graham's cause. Their governments saw Graham's advocacy of indefinite NPT extension as a cynical attempt to enshrine the United States forever as the world's leading nuclear weapons power. They had grumbled about the NPT bargain since its inception. They had heard a thousand times the argument about how the NPT made the world safer. They largely accepted the point.

But they asked an insistent question in reply: Were the five nuclear powers, and especially the United States, going to live up to their side of the deal and give up nuclear weapons for good? A Challenge From Mexico

Miguel Marin-Bosch, Mexico's chief representative to nuclear arms control talks, flew from Geneva to New York last fall scenting an opportunity to test the truth of his friend and rival Tom Graham's recent proclamations about U.S. support for the ultimate elimination of nuclear arms.

Marin-Bosch had emerged as a key leader of Third World opposition to the NPT's indefinite extension. With his walrus mustache and a mischievous twinkle in his eye, he had become one of the most popular figures in Geneva's normally staid arms control community.

Marin-Bosch wanted to hold the United States and the other four nuclear powers to the letter of their NPT pledges. He knew that total nuclear disarmament was unlikely anytime soon. But he saw the NPT's division of the world into nuclear haves and have-nots as dangerous and unjust. He thought the NPT should be extended for a relatively short period, perhaps 10 years, during which the haves should achieve a worldwide ban on nuclear weapons.

Unlike many diplomats from the developing world, he understood intimately how U.S. politics and government worked. Born in Brooklyn, N.Y., schooled at Yale and married to an American, Marin-Bosch had ended up about as American as most Americans.

Marin-Bosch suspected that Graham, by talking publicly about U.S. support for the eventual elimination of nuclear arms, was standing out on a limb within the Clinton administration. Marin-Bosch intended to saw off the branch.

Throughout the Cold War, the United Nations had hosted a dull, often meaningless session on disarmament each fall. But last November's meeting took on a new and timely importance: It loomed as a dress rehearsal for the NPT vote.

The Third World nations had traditionally submitted a resolution at the conference that closely copied the NPT's pledges on the elimination of nuclear arms. In past years, despite their NPT commitments, the five nuclear powers generally abstained or voted against the resolution. If the United States, Russia, China, France and Britain voted no or abstained this time, they would be rejecting publicly a key element in the NPT bargain at the same time that they were seeking indefinite extension of the treaty. If they voted yes, they would place themselves on record in support of a total ban on nuclear weapons -- perhaps only a symbolic declaration, given their arsenals, but one that might have an impact on public defense doctrines and key nuclear-backed security pacts such as the North Atlantic Treaty Organization.

Within the Clinton administration, Graham led what there was of a radical wing in the debate over the future of nuclear weapons. He never openly stated that he favored the elimination of nuclear arms in the foreseeable future. But like Energy Secretary Hazel R. O'Leary, he referred sympathetically to that goal in public, and he advocated decisions, such as a permanent ban on all testing of U.S. nuclear weapons, that would clearly marginalize the role of nuclear arms in U.S. national defense. He saw no harm in reaffirming the NPT pledge; after all, the NPT did not call for a ban on nuclear weapons tomorrow or the next day. It was just a goal, without a time frame.

Many other national security advisers in Clinton's administration opposed the sidelining of nuclear weapons -- and they had no interest at all in the "zero option." Pentagon doctrines routinely affirmed the continued central importance of nuclear arms to U.S. defense and alliance commitments.

Some of these advisers, including key nuclear weapon policymakers at the National Security Council, acknowledged that the role of nuclear weapons in the world was changing rapidly and that very deep reductions in the U.S. nuclear arsenal might some day be imaginable. But with Russia and China facing politically uncertain futures, the United States could not afford to let down its nuclear guard, they believed.

As to what should be said in public about the NPT pledge to eliminate nuclear weapons, these Clinton advisers supported the British and French approach: silence. The United States could win the NPT vote just by emphasizing the benefits of the treaty to smaller countries facing potential nuclear threats in the 21st century, these advisers argued.

Enlightened self-interest would lead a strong majority of nations to vote for indefinite NPT extension -- or so they assumed. A Preliminary Vote

As the NPT rehearsal vote approached last November, the Clinton administration's first response was to try to quash Marin-Bosch's challenge.

The key resolution on nuclear disarmament had been offered by India, a budding U.S. friend. John D. Holum, Graham's boss and the director of the U.S. Arms Control and Disarmament Agency, took a detour from his scheduled itinerary and flew to New Delhi to pressure the Indian government into withdrawing its sponsorship of the resolution.

After heated discussions in a conference room of the imperial-era Foreign Ministry building with the Indian foreign secretary, Krishnan Srinivasan, Holum prevailed. The Indians agreed to drop their resolution.

But as Holum was returning to the United States, Graham's colleague in the NPT campaign, Stephen Ledogar, walked into a U.N. conference room in New York to discover that the problem had not gone away -- and that one of the United States's closest allies, Japan, was the immediate cause.

Japan's ambassador to the Geneva disarmament talks, Yoshitomo Tanaka, presented Ledogar with a new resolution that mirrored India's almost exactly, calling for a public endorsement of the NPT's pledges about a total ban on nuclear weapons.

Tanaka explained that Japan's government had mixed feelings about its decision to back indefinite NPT extension in 1995. Many Japanese politicians sincerely wanted the five nuclear powers, including the United States, to live up to their NPT pledge. The Japanese public was even more adamant, Tanaka said; after all, they knew more than any people about the horrors of nuclear war.

"In a security arrangement such as the one the U.S. and Japan have, certain things are expected," Ledogar fumed, according to people familiar with the meeting. Ledogar was referring to the U.S. commitment to use its nuclear arsenal to guarantee Japanese security. Nuclear partners, he continued, ought "not to take steps, motivated by domestic politics, that are inconsistent with common security interests and arrangements."

In the corridors of the United Nations, Marin-Bosch moved in animated delight from delegation to delegation, circulating the Japanese resolution and urging a firm stand against the United States. When Japan tried to water down its resolution to please the United States, Marin-Bosch warned Tanaka that he would not win a single vote from the Third World countries. Japan restored its earlier, bolder language.

As the vote neared, cables and telephone calls flew back and forth among the U.S. Mission to the United Nations, the State Department and the National Security Council in Washington.

British and French diplomats put on a full-court press, urging the United States to join them in abstaining from voting on Japan's proposal. They said their governments would not go on record in favor of eliminating nuclear weapons, even symbolically. If the United States publicly endorsed such a pledge, it would leave two of its key allies exposed. The British and French desperately wanted the NPT to be extended -- they just did not want to talk about their own commitments under the treaty, because that would give their critics at home and abroad a way to pressure them into nuclear arms reductions.

After frantic discussions, White House officials decided to back the Europeans and spurn Japan. On Nov. 16, the Japanese resolution on nuclear disarmament sailed through the U.N. General Assembly with the United States, Britain and France among just eight countries that abstained from the vote -- alongside such nations as North Korea and Cuba.

Graham was not directly involved in the U.N. debate. He learned of the U.S. abstention while attending a conference in Dallas. An audience member asked why, if the United States supported the NPT, it had just abstained from a resolution based closely on the treaty's nuclear disarmament language. Graham, embarrassed but aware of the divided views within the administration, said he had no answer.

After the triumph in New York, Marin-Bosch hit the road, his speeches against indefinite extension bolder than ever. By last January, the Clinton administration had grown so fed up that, in the midst of the Mexican peso crisis, it lobbied the Mexican government to replace Marin-Bosch as its representative. The gist of the U.S. message, according to people familiar with the process, was: "Marin-Bosch has been a thorn in the U.S. side for 20 years. We're now trying to help with your economic problems, and we need your help with the NPT." But Mexico refused to yield to the pressure.

On Jan. 26, Marin-Bosch and Graham reunited in New York at a preparatory meeting for the 1995 NPT extension vote. Marin-Bosch played to the gallery of Third World delegates. Speaking of the five nuclear powers, he declared defiantly: "They continue to rely on nuclear weapons and do not seem prepared to give them up. . . . Quite the contrary, they are looking for ways to freeze the NPT's dichotomy between the nuclear haves and the nuclear have-nots."

At another meeting a few hours later, Graham's anger with Marin-Bosch boiled over. "I have deep respect and affection for Marin-Bosch," Graham said icily, with Marin-Bosch listening. "But I fundamentally disagree with everything he has just said." Toward a Decision One month from now, the long diplomatic struggle between Tom Graham and Miguel Marin-Bosch will have ended with the final NPT vote in New York, and the treaty will almost certainly remain standing in some form as the architecture of global nuclear security.

A weekly U.S. intelligence estimate, circulated in early March, found 79 countries firmly in favor of an indefinite extension and 15 or 16 others leaning toward the U.S. position -- the making of the 88-vote majority that the United States needs. Since then, U.S. officials say, they have confirmed enough votes to reach the majority with some to spare.

That may be enough mathematically, but U.S. officials worry that a thin majority would not provide the NPT with the political and moral authority necessary to curb the spread of nuclear arms. Some critics outside the government believe the United States should compromise with the Third World and accept some time limit on the treaty. The Clinton administration has pressed ahead, intent on preserving its bargaining position for the talks themselves.

As the heated lobbying in recent months has shown, the NPT extension is about much more than numbers. The vote is occurring, by historical coincidence, at a time of deep uncertainty around the world about the basic role of nuclear weapons in political and military affairs. Much has happened in the past two years, but many crucial questions remain.

The United States has stopped testing its nuclear arsenal -- for decades, testing has been the key to developing new weapons -- but its goal of a comprehensive, worldwide ban is unmet. At best, negotiators involved believe they may reach agreement on a global test ban by September 1996. If they fail, the world will confront new uncertainties about which countries intend to modernize their nuclear arsenals for the 21st century -- and for what purpose.

Incidents like the recent biological weapon attack on the Japanese subway system have highlighted the possibility that other terrorists may seek to acquire weapons of mass destruction. But while the Pentagon has developed a new military mission to address such threats, funding for the program is limited, confusion about its purpose remains rife, some diplomats and congressmen question its value, and U.S. military leaders are still trying to decide on the right weapons to do the job.

Meanwhile, the world's overarching strategic nuclear balance is moving in uncertain new directions. Recent contacts among U.S., Russian and Chinese nuclear missile generals and nuclear weapon designers have opened channels of cooperation closed for decades, but the ultimate effect of these collaborations on the global nuclear order remains unpredictable. The United States has helped to corral thousands of nuclear weapons from outlying former republics of the Soviet Union and move them to Russia, but that program is far from complete.

A key strategic nuclear arms control treaty, START II, remains unratified, hostage in part to deteriorating diplomatic relations between Washington and Moscow. Generals and military leaders in the United States and Russia have made important changes in their targeting computers for nuclear missiles, yet both sides still believe they need to guard against the other's ability to launch a surprise nuclear strike.

While Washington and Moscow shuffle toward each other nervously, militant states such as North Korea threaten to redefine the nuclear order on their own by acquiring nuclear bombs. Indeed, North Korea has set a deadline for later this month for fulfillment of its demands in an unfinished diplomatic deal reached last year to contain its nuclear program. Some U.S. officials worry that North Korea may again defy the NPT regime -- even as the Pentagon is struggling without clear result to determine how to deter the North Koreans and other radical governments from using nuclear bombs.

The International Atomic Energy Agency, which regulates North Korea's nuclear program in its work as the NPT's watchdog, plans to adopt a tough new inspection and control regime later this spring, but those reforms will have little effect if North Korea decides to defiantly chart its own nuclear course.

Above all, the basic role of nuclear weapons as instruments of military and political power in the 21st century remains unsettled as the NPT conference opens.

A few weeks ago, ambassadors from the five powers met for their weekly private session in Geneva to discuss whether they ought to say something definitive about the ultimate future of nuclear weapons.

At the meeting, the Russian ambassador, Grigori Berdennikov, proposed what he called "a coordinated statement" on the NPT's pledge to ban nuclear arms, according to people familiar with the meeting. Russia's government had decided it was certainly "able to confirm its obligations" in public, he said. But the British and French ambassadors declared that any such statement would be unacceptable.

Berdennikov stated the obvious: If the five powers could agree on a unified public statement about the future of nuclear weapons, it would "make our lives easier" during the NPT conference.

The Russians circulated their proposal. As of yesterday, no such declaration has emerged. Sometime over the next month, as NPT talks unfold, the positions of the five powers may become clearer. CAPTION:THE NUCLEAR NON-PROLIFERATION TREATY HISTORY * Signed July 1, 1968, in Washington, London and Moscow. Ratified by the U.S. Senate on March 13, 1969. Treaty entered into force for a 25-year period on March 5, 1970. The NPT review and extension conference at U.N. headquarters in New York will be held April 17-May 12. As of April 10, 175 of the United Nations' 185 members had signed the treaty. MAIN POINTS OF THE TREATY * The five nuclear weapon powers pledge not to transfer their weapons to other nations and to negotiate "in good faith" total nuclear disarmament and an end to all nuclear tests. * All non nuclear weapon members agree to forgo the acquisition of nuclear weapons and to accept IAEA safeguards on their nuclear facilities. * All treaty members have "the inalienable right" of access to nuclear technology for peaceful purposes. * Treaty members agree to decide by majority vote if there is no consensus whether to extend the treaty indefinitely or for another single fixed period or for a series of renewable fixed periods. THE OUTLOOK FOR THE NPT * In favor of the NPT's indefinite extension: 79 Includes the 54 members of the Organization on Security and Cooperation in Europe, seven members of the South Pacific Forum and seven Central American countries. A number of other Non-Aligned Movement members have pledged their support. They include South Korea, the Philippines, Argentina, Cameroon and Ethiopia. * Leaning toward indefinite extension: 37 Includes 21 African countries, Saudi Arabia, Colombia and Peru. * Against indefinite extension: 17 Includes Algeria, Egypt, Syria, North Korea, Nigeria, Venezuela, Indonesia and Thailand. * Leaning against indefinite extension: 23 Includes Ghana, Iraq, Laos, Mexico, Senegal, Tanzania, Vietnam and Uruguay. * Undecided: 19 Includes China, the Vatican, Kuwait, Libya, Morocco and South Africa. SOURCE: Campaign for the Non-Proliferation Treaty CAPTION: THE NUCLEAR POWERS * Tom Graham, the Clinton administration's special representative to the NPT talks: He seized on an obscure statement by President Clinton that the United States favored total disarmament and repeated it around the globe. Administration officials said his assertion was out of line with U.S. policy. CAPTION: Graham, left, speaks last fall at the United Nations on the question of extending the NPT, Marin-Bosch is at right. CAPTION: THE THIRD WORLD * Miguel Marin-Bosch, Mexico's chief representative to nuclear arms control talks: He has emerged as a key leader of Third World opposition to the indefinite extension of the nuclear Non-Proliferation Treaty. He saw the NPT's division of the world into nuclear haves and have-nots as dangerous and unjust. CAPTION: Marin-bosch, left, at the U.N. One month from now, the long diplomatic struggle between him and Graham will have ended with the final NPT vote. CAPTION: Mexico's Miguel Marin-Bosch wants to hold the United States and the other four nuclear powers to the letter of their NPT pledges. CAPTION: Arms control specialist Tom Graham worked hard to change U.S. policy to help win indefinite extension of the nuclear Non-Proliferation Treaty.