Crown Prince Fahd, long identified by American ambassadors and policy-makers as the key to stability and stronger U.S. ties to Saudi Arabia, is yeilding much of his power to other members of the Saudi royal family, according to U.S. intelligence reports.

The causes for Fahd's declining influence still are not clear to U.S. analysts. But the decline suddenly has become a major preoccupation for the Carter adminstration, which fears that the Fahd problem may be part of a potential crisis in Saudi leadership that could shake some of the basic assumptions of U.S. foreign and energy policy.

The intelligence reports and similar accounts brough back from Saudi Arabia by recent U.S. visitors add to a spreading impression in official Washington of a new fragility and unsteadiness within the 2,000-member royal family and rules the world's largest petroleum exporting country.

Coming in the wake of the collapse of Shah Mohammad Reza Pahlavi and Iran's continuing turmoil, signs of Saudi weakness and vacillation that would previously have been blips on the radar screen of policy now loom like mountains in the perception of worried Carter aides.

The administration's heavy reliance on Saudi Arabia in shaping U.S. oil and Middle East policy in its first two years appears to be diminishing as Washington reassesses Saudi stability and power in the light of the shah's fall and the new US. support going to Egypt as a result of its peace accord with Israel.

Much of the queit but intense debate within the administratiob rises from the mysteries surrounding the portly, fun-loving Fahd. He had been cultivated by the Nixon, Ford and Carter administrators as the longterm strongman of Saudi politics. But his evident lack of leadership at home and in Arab-bloc politics in recent months has earned him the label of the "Marshmallow Monarch" from disillusioned State Department analysts.

Recent copies of The Morning Digest, a secret daily intelligence summary produced for senior administration officials, have reported that new health problems appear to be keeping Fahd, 57, from functioning as the day-to-day head of government, The Washington Post has learned.

The summaries and other accounts suggest that despite his own deteriotrating health, King Khalid, 66, is taking up much of the slack left by Fahd's withdrawal. Prince Abdullah, commandor of the National Guard, and Prince Sultan, defense minister, are also reported to be exercising more authority.

Fahd became designated heir to the throne and prime minister in March 1975 when King Faisal was assassinated. Khalid, Fahd's seriously ill half-brother, came to the throne for what was predicted to be a short and ceremonial rregign that would be dominated by Fahd's determination to "moderrnize" Saudi society.

Undisputed intelligence about the constant maneuvering that goes on inside the small, secretive circle of princes who rule Saudi Arabia is rare. The Morning Digest reports stressa the speculative nature of U.S. information at this point.

But Fahd's absence from Saudi Arabia during the crucial Arab conference in Baghdad the last week in March is being taken by many U.S. analysts as conclusive evidence that he is eclipse and perhaps in disfavor with the king and other senior princes.

Explanations suggested here for his sudden trip to Madrid for "medical examinations" range from a possible return to the heavy drinking that Fahd was said to have given up upon becoming crown prince to serious political differences within the royal family over the U.S.-Saudi special relationship and Anwar Sadat's successful bid for a peace treaty with Israel.

Some U.S. officials experienced in Saudi affairs even caution that Fahd's absence and reports that he had been morose and withdrawn over the past six months could be part of a Saudi effort to shield the heir apparent from competing sets of pressure now being focused on the royal family.

Those pressures include Arab criticism certain to come if Saudi Arabia does not reduce its $1-billion-a-year support for Sadat. Saudi cooperation with Washington also will be a flashpoint of dispute.

At the same time, the Saudis face increasing conflict with the United States over the Saudi domestic commitment to keep oil production limited to an average of 8.5 million barrels to a day for the year. The administration has already angered the Saudi by insisting that production be raised and that the Saudis more actively resist price rises within the Organization of Petroleum Exporting Countries (OPEC).

Even if calculted, the maneuvering for position and influence within the family and abroad appears to be exacerbating stresses brought by the disappearance of the strong and steady Faisal, Arab uproar over Sadat's peace bid, and the religious-led revolution across the Persian Gulf in Iran.

For the first time since the Saudi Air Force was purged in 1969 after an abortive coup, foreigners in Saudi Arabia are beginning to hear of discontent within the armed forces over which the royal family has establised tight control. The reports are extremely sketchy, but disturb U.S. officials.

Prince Abdullah's National Guard is the key internal security unit, protecting the kingdom's main cities, oil fields and communications facilities. The guard is a deliberate counterweight for the army, commanded by Prince Sultan and stationed on Saudi Arabia's border. Abdullah and Sultan appear to be serious rivals for power behind Khalid and Fahd.

The confusion in the administration surrounding Saudi intentions is compounded by reporting cables from the U.S. embassy in Jeddah that "are as uncritical and self-serving for the Saudis as the reporting on the shah was from Iran last year," according to one U.S. official familiar with them. The embassy is headed by a Carter political appointee, John West, the former governor of South Carolina.

U.S. analysts have been closely watching suggestions of serious splits between Fahd and the rest of the family over policy toweard the Arab world and the United States since November 1977, when Sadat stunned the world by flying to Jerusalem and beginning his effort for the peace treaty that was signed last month in Washington.

Until then, the Saudis had treated Sadat's survival as a matter of their own national security. They fear a return to the assertive Arab nationalism and dependence on the Soviet Union that marked the rule of Sadat's predecessor, Gamal Abdel Nasser, who openly sought to topple the Saudi royal family.

But their support for Sadat became ambivalent after the Jerusalem trip. At the Baghdad summit conference last November, Fahd agreed to a sharp denuciation of Sadat that Foreign Minister Saud Faisal and other officials had told the United States the Saudis would not accept.

This reversal shook the Carter administration's confidence in the Saudis, whom the White House had viewed as a strategic partner with enough economic influence to help stabilize the Middle East and other Third World areas. Reports that Fahd went into a funk after the 1978 Baghdad conference further undermined U.S. confidence.

Administration experts on Saudi Arabia still do not agree on the political meaning of the royal family's oscillations over the past six monthes. There is some evidence, however, that Fahd argued that Saudi Arabia had to move away from Sadat - at least publicly - and try to mend relations with Iraq and Syria, which he saw emerging as the dominant forces in the region after the disintegration of Iran's army and Egypt's effective withdrawal from the Arab political and military front.

Moreover, some analysts believe Fahd was behind the tactical decision to extend a feeler to the Soviet Union on improving relations, at a time when the Carter administration was pressing the Saudis to support Sadat more openly.

Part of the U.S. effort was to get Fahd to come to Washington to discuss the Camp David accords, but the crown prince abruptly canceled his trip in March for whatt the Saudis suggested were political reasons. The Carter administration's conflicting public explanation that Fahd was ill drew a sharp Saudi rebuke.

His sudden trip to Madrid has rekindled the medical-political dichotomy. There are theories that Fahd was bundled out of Riyadh, which has possibly the world's most expensive and modern hospital, by a royal family anxious to get him out of the way during the second Baghdad conference. There is also the Machiavellian view that Fahd himself engineered the trip for political self-protection.

U.S. officials concede that they do not have enough hard information to make a conclusive choice between the various explanations. But the theories continue to feed into a perception of trouble in Saudi Arabia that, however far from reality it may be, is beginning to affect policy planning in Washington. CAPTION: Picture, CROWN PRINCE FAHD. . . power appears to be waning