The enormous power that has settled uneasily onto the shoulders of an elderly and infirm king, his two determined but mutually distrusting half-brothers and their 2,000 uncles, rousing and other male relatives is now thrusting Saudi Arabia into the front line of world politics.

Taken for granted or even ignored by past U.S. administrations as a policy pygmy in its own region. Saudi Arabia and its royal family have in four years moved swiftly toward the center of American calculations and objectives abroad.

That movement is beginning to affect U.S. ties to its two strongest traditional allies in the Middle East, Israel and Iran, who now share their positions as American surrogates in the region with Saudi Arabia. The Carter administration is stepping up American reliance on Saudi Arabia in foreign policy, just as Iran and Israel are seeking, for separate reasons, to become less dependent on their ties to Washington.

Moreover, the Saudis are using their still-growing oil wealth to counter radical trends and Soviet influence in the Middle East, Africa and oven Western Europe in ways that would have been unthinkable for the kingdom at the beginning of the decade. Increasingly, they are able and willing to act in areas where post-Vietnam America is reluctant to become more deeply involved.

Saudi power and influence in America also are rising in geometric progression. The United States relies on Saudi Arabia for 25 per cent of its imported petroleum supplies. The Saudis have put an estimated $40 billion into the U.S. economy in the past four years, giving them enough leverage to affect U.S. interest rates and the strength of the dollar on foreign foreign exchange markets in the unlikely event they should choose to do so.

"We are reaching the point were we are more dependent upon them than they are on us," says one worried American diplomat who has much exprience in the Middle East and a great deal of sympathy for Saudi goals. "No matter waht good friends they are, that is an unhealthy position for us."

This qualitative change may be the most vital component of the transformation of global power relationships since the oil exporting countries dictated an end to the cheap energy era in 1973. Today, Saudi Arabia's friends can argue that the U.S.-Saudi link ranks only behind the U.S.-West German alliance and Washington's ties to Tokyo in containing Soviet influence and maintaining political and economic order in the world.

That is a staggering prospect for a country that emerged as a unified nation-state only in 1932, that probably has a permanent population of fewer than 5 million and that posesses an army smaller than those of Peru or Belgium.

The Saudis themselves do not call attention to this change. The tightly knit group of emirs, princes, American-educated Rh.D.s and Bedouin tribal chiefs who make up the royal family have not sought a world role and are still uncomfortable with it. They strongly resisted American efforts earlier in the decade to get the Saudis more involved outside their borders.

But since mid-1975, when the assassination of King Faisal brought a new ruling team to power, Saudi Arabia has moved from that passive and reluctant posture to an active, outward-looking stance. Saudi foot-prints now turn up in regions and on issues they once would have skirted. Cases in point:

When Congress refused last year to appropriate $50 million in emergency U.S. aid to the help Zaire's President Mobutu Sese Seko confront a Soviet-backed regime in neighboring Angola, the Saudis quickly stepped in and gave Mobutu the money. This spring, Moroccan troops financed by Saudi Arabia flew to Zaire to help put down a revolt against Mobutu.

By continuing to underwrite Egypt's economic and military development at a cost of several billion dollars a year, Saudi Arabia has made possible Anwar Sadat's daring attempt to negotiate a final settlement for the Arab world with Israel.Egypt, Syria, Jordan, the Palestinian and Lebanon must nervously watch Saudi reaction as they move toward or away from the negotiating table. This makes Saudi Arabia a silent but essential participant in the process.

In sharp contrast to their past fence-sitting on inter-Arab quarrels, the Saudis called the factions and countries involved in the Lebanese civil war to the Saudi capital, Riyadh, last year to arrange a settlement. The energetic young Saudi foreign minister, Prince Saud Faisal, opened the meeting by calmly advising his Arab "brothers" they would not be allowed to leave the country until they had come to a binding agreement.

Saudi Arabia took the initiative in formulating a plan and putting up the money to get Somalia to break its military alliance with the Soviet Union. Saudi sources say Saudi Arabia has pumped $200 million into the strategically located Horn of Africa to enable the Somalis to purchase arms in the West to replace Soviet weapons. "It is a bargain rate," said one Saudi.

By providing South Vietnam and Taiwan with oil priced at pre-1973 rates, the Saudi government saved those two Asian, anti-Communist governments hundreds of millions of dollars.

(The help to Taiwan was given in part because of King Faisal's regard for the late Generalissimo Chiang Kai-shek. But Faisal's help for the Thieu government in Saigon was purely to shore up a regime fighting communism and in response to pleas originated or endorsed by then Secretary of State Henry A. Kissinger. When President Nguyen Van Thieu appealed to Faisal, through Kissinger and the State Department, for massive cash grants as the end of the war neared in March, 1975, the Saudis Pigeonholed the request. Recent accounts suggesting that Faisal initiated the idea of cash aid for Saigon are incorrect, sources close to the talks report.)

National oil companies in France, Italy and Spain - countries with active Communist parties seeking a share of power - have been offered some pricing discounts on limited supplies of Saudi oil. Saudi monetary officials have made special loans and bank deposits to these countries and diverted billions of dollars in lucrative contracts to them, in large part on a political basis. The Saudi money not only bolsters countries they see as threatened by Eurocommunism, but also rewards Europeans who have adopted a more pro-Arab policy in the Middle East.

Such moves go far beyond the traditional Saudi policy concerns of helping establish a zone of "reasonable" (i.e., moderate to conservative, Pro-Western) Arabs near their borders. In selected regions, the Saudis are now playing what American officials call "a facilitating role" in helping other governments withstand leftist pressures for quick change.

But there are common threads connecting the new activism and the traditional concerns. The dominant Saudi policy goals continue to be protection of the royal family and the American-managed oil fields that have brought it the world's second-largest store of foreign currency reserves, surpassed only by West Germany's.

After defeating its domestic rivals for control of the Arabian peninsula and giving its name to the country in 1932, the house of Saud became convinced that the virus of Arab radicalism that could destroy its rule would be brought into the region only by non-Moslem, foreign forces. The family has consistently identified communism and the Soviet Union as the most dangerous carriers of the virus, and its actions are aimed at pushing them away from the borders of Saudi Arabia and its closest allies.

These goals coincide almost exactly with those of the United States, American policymakers say in remarks that suggest Saudi strategic objectives resemble those of the United States more closely than those of any other country.

The Saudis clearly see an implied quid pro quo, with the United States protecting the royal family and keeping the Soviets and radical Arab states at bay, while they assure both the flow of oil to the United States and a more general economic stability.

The only obvious point of conflict is over Israel, which Saudi Arabia has identified as the other great threat to its existence.

Another Arab-Israeli war could produce pressures that would taopple the royal family. Arab analysts and Israeli supporters in the United States seem to agree that this message has been noted by President Carter, who has identified energy as the most urgent American problem and who has moved closer to publicly endorsing Saudi concerns about the Palestinian problem and Israel than did any of his predecessors.

"Energy - and that means Saudi Arabia - is the bottom line for a settlement in the Middle East for this administration," says a State Department official. "We spend more time writing papers now on what the Saudis will do to facilitate an agreement than any other long-term prospect."

Carter put it this way during a visit to Washington this year by Crown Prince Fahd: "I don't believe there is any other nation with whom we've had better friendship and a deep sense of cooperation than we've found in Saudi Arabia."

The vitality and overriding importance of Saudi policy for American objectives are of very recent origin and perception. Faisal enjoyed discussing the demonology of world communism with President Eisenhower and then Secretary of State John Foster Dulles, but this did not translate into important policy changes.

With oil cheap and plentiful and Egypt's Gamal Abdel Nasser successfully promoting himself as the wave of the Arab future, the Kennedy and Johnson administrations put Saudi Arabia at the periphery of their policy concerns. President Nixon in his first five years put all of his strategic reliancce in the Persian Gulf on his friend, Iran's Shah Mohammaa Reza Pahlavi, whose military buildup was encouraged under the Nixon Doctrine of regional powers carrying out American security objectives.

The 1973 oil embargo and price increases focused the minds of Nixon and Kissenger on the slumbering petroleum giant, and the Secretary of State increasingly courted, consulted and cajoled the Saudis throughout his term of stewardship.

But it is under the Carter administration that the relationship is coming to full flower, not only because of the increasing importance of Saudi Arabia as the only country that can produce enough additional oil to meet America's future import needs, but also because the royal team that has succeeded Faisal has shown a willingness to use the enormous power it inherited.

The 64-year-old monarch, King Khalid, weakened by open heart surgery in 1972 and more recent operations on his left leg, has turned much of the policymaking over to his 54-year-old half-brother, Crown Prince Fahd. While they are not close, Fahd and Prince Abdullah Abdel Aziz, the commander of the Bedouin units that make up the national guard, have established a modus vivendi in running both the country and the extended royal family that has sprung up from the network of marriages designed to unify the country's clans.

Fahd has taken active charge of foreign policy. Shortly after assuming office, he startled an American visitor accustomed to the subtle, Byzantine-like style of Faisal by giving a direct and personalized vision of things to come: "I intend to get the Russians out of Somalia. My policy will be to help the moderate forces in South Yemen. I will help the Sudan resist Communist subversion."

Fahd's principal tactician is Foreign Minister Saud, Faisal's son. Picking up the style of jet-age diplomacy, he has been on the road almost constantly this year, logging as many miles as Kissinger at his most shuttling pace. While Saud does not appear to have a dominant role in setting the policy he articulates, he evidently has been given special responsibility in Africa. Kamal Adham, the gray eminence of Saudi policymaking, continues to be paramount in handling Arab accounts.

"The efforts of Saudi Arabia have increased because of our ability has increased," Saudi said in a recent interview with The Washington Post.Using the same phrase employed by Carter's advisers when outlining Saudi policy - "coincidence of objectives" - the Princeton-educated prince said, "The United States knows what we are doing - I am sure the State Department knows about it."

A State Department official goes further: "The Saudis are very sensitive to what we do and do not want. They have the perception that they are doing things that the U.S. is not able to do now."

While the coopertation continues to grow, it is not total. The Saudis are increasingly establishing their own objectives and still do not respond of the burden in the changing global power equation.

"The Saudis have established their own shortlist of a dozen or so deserving African countries who deserve aid, and that list includes only our friends," says an American official who has watched the growth of the U.S.-Saudi alliance. "But nothing the Carter administration could do would induce the Saudis to put Mozambique's leftist government on that list. We send in dozens of 'letters of recommendation' for deserving friends that the Saudis just never act on. And they seem to be getting irritated that we don't concentrate on a few cases where help is most important."

And American support for Israel remains a potential flashpoint in the relationship. Just after Sadat launched his offer of direct peace talks with Israel, the White House, scrambling to catch up with the action, instructed Ambassador John Carl West to go to Fahd and ask him, in effect, to lean on the Syrians to get them to the peace table with Sadat.

Fahd, who had been quietly laboring to get the Syrians to show restraint, did not appreciate the presumption of the message, especially coming from the Unites States. He politely but pointedly reminded Ambassador West that Saudi Arabia was still waiting for Washington to move Israel to reach a settlement with the Arabs.

But the mutual dependence that continues to grow between Riyadh and Washington overshadows these policy wrinkles.

The four to five dozen sources interviewed for this series repeatedly used the same description of the relationship: "Big brother to little brother." The implication was clear in each case.

"The Saudis know that the prospect of radicals overthrowing the family and putting their foot on the lifeline of oil to American markets is just unacceptable to Washington, which would have to take drastic action," said one Foreign Service officer. "For them, American policy toward Saudi Arabia is defined by what American policy toward the family is. That is the strongest commitment they would want."