The Atlantic Alliance is in trouble.

That is a familiar judgment and a recurrent story in an American-European relationship that has suffered, and surmounted, philosophical, political, economic and military differences on many occasions in the past three decades.

This time, in the view of Washington officials and private experts, the trouble is more serious than usual, for several reasons:

* The worst worldwide recession since the 1930s, with soaring unemployment rates on both sides of the Atlantic, has imposed sharp limits on the resources, flexibility, political strength and common purpose needed to surmount disputes. It cannot be forgotten that while they are allies against the threat of Soviet expansion, the western European countries and the United States are also leading economic competitors, and are among each other's major markets.

* Serious differences are now spread across a much broader front than usual, including nuclear strategy, East-West political and economic relations, the Middle East and Central America as well as flash-point economic issues involving trade in steel and farm commodities.

* Beneath the surface of specific troubles are basic disagreements on the nature and vulnerability of the Soviet Union, and on the proper role of government intervention in market economies. These gaps have been widened by the coming to power of a U.S. administration whose strongly held views on these subjects are well outside the European consensus.

Heading the long list of disputes within the alliance, many dating back to previous U.S. administrations, is the unexpected and, in the European view, unnecessary flare-up that has come over the planned Soviet natural gas pipeline to western Europe.

A single decision by President Reagan seven weeks ago brought the pipeline issue, and U.S. relations with the allies, to the point of crisis.

The Reagan administration has long opposed construction of the Yamal pipeline on grounds that it would unwisely increase western Europe's energy dependence on Moscow and that the Soviet Union's earnings from the natural gas sales would add to its national strength.

One of the sanctions Reagan imposed against the Soviets Dec. 29, following the imposition of martial law in Poland, was to bar U.S. firms from supplying equipment for the Soviet project. At the time he said unspecified "further steps" might be necessary if repression continued.

On June 18, the president took those additional steps, forbidding European subsidiaries of U.S. firms or European firms using U.S.-licensed equipment from participating in the pipeline project.

That action infuriated the allies, who viewed it as a violation of settled contracts and commitments, of European sovereignty and of the political tolerance that undergirds the Atlantic Alliance.

Less than two weeks before, Reagan and the European leaders had spent much time at the Versailles summit meeting hammering out a common position on East-West economic relations. But according to a U.S. participant, so much time was spent on very general language, especially the need for "commercial prudence in limiting export credits" to the Soviet Union, that the specific issues of the pipeline were ignored.

There is, in addition, no indication that the probable reaction of the allies was seriously taken into account in Reagan's decision. Then-secretary of state Alexander M. Haig Jr. had argued for months against pressing the allies further on the pipeline, saying it would not succeed, but by June 18, the weekend before his resignation, Haig had lost the confidence of William P. Clark, the presidential national security adviser.

The White House meeting to decide the pipeline issue was held while Haig was in New York conferring with Soviet Foreign Minister Andrei Gromyko, and there are indications that maneuvering between Haig and Clark played a part in the decision-making.

The allies' certain objections to a U.S. attempt to extend the pipeline prohibitions to subsidiaries and licensees abroad was mentioned during the Cabinet room meeting by the State Department representative, Undersecretary of State Lawrence S. Eagleburger. But this reportedly was brushed aside as unimportant by Secretary of Defense Caspar W. Weinberger, the leading administration foe of the pipeline project.

Reagan, in announcing his decision to the meeting, concentrated heavily on his desire to carry forward his Dec. 29 sanctions, as a matter of principle, in the absence of progress toward liberalization in Poland. Nothing was said, according to an informed account, to suggest that Reagan anticipated a major blow-up with the allies, and top officials have since conceded that the very strong outcry took the White House by surprise.

Since the Polish events last winter, Reagan had been fascinated by reports of the economic weakness of the Soviet Union, which he considers a decaying regime that may fade from view. In response to his expressions of interest, the Central Intelligence Agency has been sending Reagan a special weekly report about Soviet economic woes for several months. This, too, was in the background of Reagan's pipeline decision, but there is no evidence that he referred to it in the fateful White House meeting.

Since the decision was announced, all four of Reagan's European summit partners--Britain, France, West Germany and Italy--have made it clear that they will defy the U.S. ban as it applies to companies under their control. France went so far as to order its companies to honor their pipeline contracts, despite U.S. regulations. The British are telling their companies not to comply with "an attempt to interfere with existing contracts" and "an unacceptable extension of American extraterritorial jurisdiction . . . which is repugnant in international law."

Despite several meetings and studies on the subject, there is no clear plan at the White House or State Department for resolving the pipeline issue. Several officials made the point that Reagan, having made and announced his decision, cannot be expected to reverse himself simply because the Europeans are protesting. Nor does there seem any likelihood that the Europeans will back down.

In theory at least, Polish government action to ease the repression there would provide a justification for Reagan to ease the sanctions. Hardly anyone sees such Polish action in the short run, although the president surprisingly told corn growers in Des Moines Monday that he is "somewhat encouraged by indications martial law may be relaxing."

It did not escape European notice that Reagan's "encouragement" was spoken to justify his decision, popular among hard-pressed U.S. farmers, to sell more grain to the Soviets. But Reagan's view was much bleaker about the prospects in Poland when justifying the extended U.S. measures against the pipeline, which is politically important in western Europe.

One of the most serious aspects of the pipeline dispute is that it is likely to persist for many months in legal action and political debate, souring other aspects of the Atlantic Alliance relationship. Some officials seem to believe there are already signs of a spillover from the dispute into harsher French attitudes on international questions, including Central America.

"This can be a running sore that doesn't heal," a concerned U.S. official said. "This is not the death of the alliance, but it is serious. It is potentially debilitating over time."

Veterans at dealing with the Atlantic Alliance argue that the present problems, while serious, must be seen in the historical perspective of almost unrelieved disagreement on one point or another.

West German Ambassador Peter Hermes, for example, recited a long list of disputes including the "agonizing reappraisal" of U.S. strategy by John Foster Dulles in 1953, the "chicken war" between the United States and Europe in the late 1950s, the Nixon economic shocks of 1971 and President Carter's nuclear decisions in the late 1970s.

"We always have had problems, and we always have taken them seriously," Hermes said. "We don't have to yell like Cassandra that this time it is fatal. It is a misconception to think that it is."

Assistant Secretary of State Robert D. Hormats, who is preparing to return to private life after more than a decade as a top U.S. expert on economic affairs, said the degree of friction with Europe today is similar to that following President Nixon's unilateral 1971 decisions to abandon the gold standard and impose a surcharge on imports to the United States.

"The difference is that now the problems are complicated by the fact that economies are weaker, which makes management more difficult. Internal pressures are greater," Hormats said. While "there is a serious lack of consensus on a number of important issues, including differences in philosophical approach," Hormats also believes that the fundamental interests of the United States and the European countries remain closely allied.

In the flush of anger over the pipeline decision, France's outspoken Foreign Minister Claude Cheysson declared in a widely quoted remark that "a gradual divorce is taking place between Europe and Washington--we are not speaking the same language any more--and this marked incomprehension is serious." Later, however, European statesmen sought to cool the dispute with the time-honored observation, subsequently endorsed by Reagan, that this is "a family matter" and that the family is still together.

With mutual tolerance stretched so thin and so many divisive issues in the air, there would seem to be little room for additional strain from additional disputes, and some U.S. officials expressed the hope that the pressures on the alliance would now encourage a spirit of compromise that could help to settle existing troubles.

In this light, U.S. Steel Corp.'s refusal Friday to accept a negotiated settlement of the U.S.-European steel import dispute is considered a discouraging sign. Three days of intense discussions between Commerce Secretary Malcolm Baldridge and European Common Market officials had produced a plan to resolve the dispute without divisive and precedent-setting U.S. legal action.

U.S. Steel Chairman David M. Roderick rejected the plan as "neither fair nor equitable" several hours after a White House statement saying that Reagan took pleasure in the agreement, believing that it "could lead to a resolution of steel trade problems." Reagan hailed the "spirit of understanding and cooperation" on both sides of the Atlantic which made the agreement possible, but the American steelmakers wanted more than the administration delivered. The U.S. industrialists apparently felt they could get more by holding out, whatever the cost to the Atlantic Alliance.