In the colorful argot of the oil business, they are known as "elephants," the giant oil fields that pump hundreds of thousands of barrels of oil a day for years and years. The huge Prudhoe Bay field in Alaska is an elephant. The Middle East is full of them.

And so is the Soviet Union. With known oil reserves twice those of the United States and perhaps ultimately as great as those of Saudi Arabia, the Soviet Union has become the new frontier for the oil industry's ivory hunters.

Over the past couple of years, Western oil companies have been invited into the Soviet oil fields for the first time in decades. Moscow hopes the companies' considerable financial and technical resources can help check a sharp slide in Soviet petroleum production that threatens the nation's best source of hard currency. For the companies' part, they see a chance to take a crack at what may be the last of the world's elephants.

"The geologists just look at that country and they go crazy," said Chevron Corp. Chairman Kenneth T. Derr, whose company appears close to signing an agreement to develop an oil field near the Caspian Sea that holds more oil than Alaska's Prudhoe Bay. If the deal goes through, half of the oil pumped would fill Moscow's increasing needs and half would be Chevron's to export.

But along with the great potential comes considerable political risk. As Western oil companies take advantage of the Soviet Union's new openness, they are finding themselves caught in the maelstrom of Soviet politics: innocent but interested bystanders in the bitter struggle between the Kremlin and the nation's republics over the course of economic and political change unleashed by Mikhail Gorbachev. The changing political winds and confusing jurisdictional disputes are combining with a virtually nonexistent framework for Soviet business transactions to make it difficult for Western companies to strike deals.

"In the last two or three months a new dimension has been added to doing business in the Soviet Union," said William T. Archey, international vice president of the U.S. Chamber of Commerce. "Most companies had been hedging their bets by dealing with both the republics and Moscow, but clearly tipping toward the republics. Now they are concerned that agreements reached at the republic level will not be able to be implemented {as Moscow reasserts the power of the central government}. It is no longer clear."

It is a situation that might cause many companies, especially those with smaller potential gains, to despair. But when it comes to dealing with the Soviet Union, the oil companies are in a special category. The risk may be high, but their payoff may be even higher.

"The potential is too big to ignore, the opportunity is too big to ignore, but I think a prudent operator will just have to be patient," said Lodwrick M. Cook, chairman of Atlantic Richfield Co., which hopes to go prospecting for oil off the Soviet Union's far eastern tip. "We just have to kind of watch developments and take it slow and see what comes out of all this. This is not a time to make huge commitments until you can see what will {happen} on the political scene."

The companies can afford to bide their time. The oil reserves being made available to them in the Soviet Union truly are elephants, perhaps the last remaining undeveloped ones on Earth. The Soviets have proven reserves of 58.5 billion barrels of crude oil -- and even more natural gas -- and already are the world's biggest oil producers, at 11.4 million barrels a day. The nation is full of vast unexplored-but-promising areas for oil production as well. By comparison, the United States has 26.5 billion barrels of proven reserves, and Saudi Arabia has 170 billion.

'You Know the Oil Is There' And unlike a lot of oil prospects, many of the Soviet fields are hardly speculative. Soviet engineers have confirmed the existence of vast quantities of oil that need only be tapped and shipped, thus slashing the time needed to bring the fields into production.

"You know the oil is there. They've already found it," said Martin G. Pranga, manager of foreign affairs at Chicago-based Amoco Corp., which is negotiating to produce oil in western Siberia. "What they're asking for is the financial assistance and the technical knowledge to develop the property."

That could mean a rapid payoff for the industry. Where companies might normally expect to spend years in exploration and development before getting a big new field on line, production from Soviet fields could be available in a matter of months once final agreements are signed.

While technical factors may make the cost of pumping Soviet oil fairly expensive, the companies will save billions on exploratory costs and will enjoy the benefits of huge production volume because of the size of the fields. "The payoff is in the sheer numbers," said an official of Phibro Energy Inc., a member of the American "White Nights" joint venture that expects to begin oil production in western Siberia in a couple of months. "We're looking at wells that will produce 1,000 barrels a day here, and we're not looking at just a couple of them, we're looking at hundreds of them."

No wonder, then, that Derr says, "If it works, the potential is great enough to take the political risk."

About a dozen Western oil companies are jockeying for opportunities to do business in the Soviet Union. Many are in the most preliminary stages, having signed "protocols" with Soviet officials that amount to agreements to agree to negotiate. Others are farther along and hope to begin modest exploration and production activities later this year: Among these are Total Petroleum of France and the White Nights venture, which includes a Houston company, Anglo-Suisse, in addition to Phibro, a division arm of Wall Street brokerage Salomon Brothers Inc.

Some companies, concerned about the unsettled Soviet political situation, are sitting things out, however. Exxon Corp. says it has not signed any negotiating protocols, while a spokesman for Fairfax-based Mobil Corp. said, "I would characterize our efforts as gathering data to identify what opportunities might exist for us."

Of all the Western oil companies with interests in the Soviet Union, Chevron's project has perhaps the most dramatic immediate promise.

The company has been negotiating for two years for access to the massive Tengiz field in the Kazakh republic at the northern tip of the Caspian Sea. Tengiz, which today is in very limited production, is believed to hold 25 billion barrels of oil, of which perhaps 15 percent to 30 percent could actually be produced using current technology, according to Richard Martzke, president of Chevron Overseas Petroleum Co.

Chevron hopes to strike a deal similar to those being sought by other companies: It will supply technical expertise and billions of dollars in capital investment for producing, processing and shipping facilities, in exchange for rights to half the oil it produces. Actually, Chevron would not receive Tengiz crude because there is no pipeline system to move it to a port from which it could be shipped abroad; instead, Tengiz oil would be consumed by the Soviets, and Chevron would export an equivalent amount of oil from elsewhere in the nation.

A few weeks ago, Derr said he thought the company could have an agreement wrapped up by the end of January. But Martzke now says a deal still is a few weeks away.

The Chevron negotiations seem to have gotten hung up on the same political problems that make Western access to Soviet oil as frustrating as it is tantalizing. These problems lead normally tight-lipped oil executives to grumble openly about the difficulties of doing business there, although they do so secure in the knowledge that the Soviets need their money and expertise as much -- if not more than -- the companies need Soviet oil.

"It is an enormously difficult bureaucracy," Pranga said. "It's an extremely difficult system."

The Political Divide The biggest problem, industry officials and analysts say, is the deepening political divide between the central government in Moscow and the leaderships of the individual oil-bearing areas -- particularly the Russian Republic, in which 80 percent to 90 percent of known Soviet oil reserves are located. Governing bodies at all levels are claiming sovereignty over the oil reserves, forcing companies to negotiate multiple agreements and hope that one or more pans out. "We feel that's the best insurance policy going," said Harold Zimmerman, vice president in charge of Texaco Inc.'s European division, which is handling the oil company's negotiations for oil-producing rights in the Timan-Pechora Basin, near the Arctic Circle.

As the tensions between Moscow and the republics increase, as manifested by the recent unrest in the Baltics, the oil companies' negotiations are becoming, if anything, more difficult. Nationalistic local and regional governments are clamoring for greater shares of the revenue from their energy reserves, setting up a tug of war with the central government and its need for the hard currency that oil exports can generate. The companies are caught in the middle.

Chevron's plans apparently have become snagged by a dispute between regional and national authorities over their shares of the revenue from the Tengiz field. "They don't have the principles in place to make the kind of distribution of wealth within the country that democratic, market-based economies have in place," Martzke said.

Also frustrating, oil executives say, is the Soviet Union's virtually nonexistent business system. The nation's business and tax laws are primitive, there are no formal trade agreements with the United States that the companies can fall back on and even accounting principles are not standardized.

"Part of the problem for oil companies ... is working out a framework through which they can make investments," said Lucian Pugliaresi, a former National Security Council official who now is a Washington consultant.

Another recent development also has given some oil executives pause: the announcement late last month that the Soviet security police, the KGB, had been given authority to review dealings with foreign companies. So far, industry executives say, they have seen no direct effect, but the potential for interference is troubling.

Yet even as they gripe about the problems of dealing with the Soviets, oil industry officials say they are not really grappling with anything they haven't seen before as they have negotiated for oil rights around the world. Much of the world's most attractive oil reserves are in areas of political instability, and oil companies have learned how to ride out such turbulence.

"Oil companies are very accustomed to doing business where political risks are rather high," said Robert Ebel, a Washington-based analyst for Enserch Corp., an energy conglomerate. "This is sort of the nature of their business."

And while the recent tumult in the Soviet Union has led companies in some other industries to pull back or reduce their plans for Soviet investment, oil companies still are pressing forward -- encouraged, no doubt, by a potential payoff much larger than those available to virtually any other industry doing business there and by the knowledge the Soviets badly need their help.

"The worse the production situation becomes, the better the terms become," said Cristina Haus, a New York oil consultant. "They're using 1950s technology. They're desperate for foreign technology."

Little Investments So Far Should the situation worsen to a point that negotiations between the Western companies and the Soviets break down completely, the companies have little to lose beside the chance to tap big new oil reserves. Upfront investments by the companies so far have been minimal -- "nothing more than airplane tickets and hotel rooms and a few meals," as one oil executive put it. "We have not entered the capital expenditure part of the project yet."

Most experts believe it will take a virtual political catastrophe to drive the oil companies away, although the current political instability may slow negotiations.

"It's a huge opportunity out there, it's enormously tempting, but it also has an enormous risk to it at this point, and I think that's the dilemma for everybody ..." Pranga said. "We at least remain confident over the long term, but I can't tell you we think it will be resolved a year from now and that three years afterwards we'd have oil coming out of the Soviet Union. That's impossible."

"We're dealing in an environment where politics can change the direction of the venture, so we're keeping our eyes wide open," said a Phibro executive, who asked not to be identified.

"So far, we haven't been slowed down by this apparent shift to the right. We feel that no matter how things shake out, the Soviet Union is going to have to export oil for hard currency if they want to participate in the world economy. ...

"I like to think that they have something to lose here, too, if it falls apart."

Staff writer Stuart Auerbach contributed to this report.