Events all over the Mideast now underline the danger of basing large international interests on the fate of single leaders.

The troubles of the shah of Iran present only the most obvious case in point. The recent behavior of the Saudi leader, Prince Fahd, at the Baghdad summit conference provides another example, Here in Cairo, as the slowdown in the Washington peace talks indicates, there is at least an incipient problem with Egypt's President Anwar Sadat.

The shah began gathering all power into his hands after his restoration to the throne, thanks in part to the Central Intelligence Agency, back in 1953. In time he came to determine foreign policy in every detail, to hold sway over all the security forces, and to dominate the making of economic and social policy.

For a brief period - in the early years of the Kennedy administration - the United States pressed him to democratize his regime. One result was the land reform that he later came to claim as his own. But President Johnson and, even more, President Nixon found in him just the kind of ruler they killed, and showered him uncritically with American blessings.

By the time President Carter reached office, there was no good alternative except working through the shah. Heavy-handed pressure on him to relax internal-security measures proved counterproductive. Indeed, lifting the lid made a major contribution to the troubles that began last January and now threaten to topple the regime.

For the time being, giving maximum support to the shah is the ony feasible American policy. The alternatives - military rule or an "islamic republic" - would yield chaos in a country critical to the world's oil needs.

But if the shah lucks out again, the United States should take its distances. Washington this time ought to insit on slow but sure progress toward a limited monarchy and a sharing of power among other persons and institutions.

In the case of Prince Fahd, he emerged as the true ruler of Saudi Arabia only after the assassination of King Faisal. Neither President Nixon nor President Ford had occasion to depent upon him. But Jimmy Carter made Fahd "out man" in Riyadh for both oil and peace in the Mideast.

In the case of oil, Fahd began backing off early last year. The sign of the switch was an unceasing flow of mysterious stories about bad weather in the Persian Gulf, low pressure in the oil fields, erosion of the pipes and that sort of thing. They added up to a typically Saudi - that is to say, non-confrontational - way of curbing planned expansion of oil production, and thus preparing the ground for a round of price increases.

As to backing the peace process, Fahd kept saying things that identified him as what the Carter administration is pleased to call "a moderate Arab." But when the test came at the Baghdad summit last week, he buckled. His presence there, his support of a resolution condemning the Camp David accords between Israel and Egypt, and his increased financial backing for Syria and the Palestine Liberation Organization all show that, in words used by President Sadat in an interview with me here in Cairo, Fahd has "gone over to the other side."

As to Sadat, he is the leading states-man in this part of the world. He has divined what his country needs (peace), figured out how to get it (through the United States) and moved dramatically (in the Jerusalem visit and at Camp David) toward his objective.

But his latest successes have been accompanied, apart from the usual backing and filling, by a curious change in personnel. In the last two weeks, the president has put on the shelf three of those who were once closest to him - Gen. Mohammed Abdulghani Gamassy, the former prime minister, and Sayed Marei, the former speaker of the assembly.

The replacements are relative unknowns parachuted into place by Sadat. The official explanation is that, with a new era of peace in the offing, there is need for new blood. Another view is that Sadat is flying solo and likes it. So he has shelved those who knew him well enough to argue, and put in their place men prepared to leave all the controls to him.

If that is the case, there is true cause for concern. For no man is big enough to make peace in the Mideast alone.