The courtship of Hosni Mubarak

Americans, Russians, Arabs, and Israelis, in accidental alliance, all seem to be giving Egypt's new President what he wants most: a little breathing space. Sooner or later, the problems and pressures inherent in the Egyptian-Israeli peace process will reemerge. Hosni Mubarak, like his slain predecessor, will have to deal with them. The outside world, at least some of it unfriendly, will be watching.

But for the time being, most of the outside world wants to be Hosni Mubarak's friend. Virtually no one, at least, seems to see much point in courting his enmity.

Of particular importance for the Egyptians are signs of support from Saudi Arabia, the key Arab petropower.

In a move unthinkable before Anwar Sadat's assassination, one of the Saudis' government-controlled newspapers has tacitly, if perhaps temporarily, accepted the Egyptian-Israeli peace process.

''We do not and must not expect President Mubarak to abrogate the Camp David agreements at this time, for a number of reasons understood by those acquainted with international convention,'' said the newspaper, published in Medina, Islam's second-holiest site.

Saudi Crown Prince Fahd is also said to have expressed backing for Mr. Mubarak's person and policy in talks with West Germany. The Saudis later denied the report, which came fron an official Bonn spokesman. But most Egyptian officials and diplomats here assume the West Germans didn't misquote the Crown Prince, and that the denial was for the sake of Saudi appearances in the Arab world.

Given President Mubarak's immediate priorities, it probably doesn't much matter whether Crown Prince Fahd said what Bonn says he did.

Nor, for instance, does it matter whether the Saudis' ambitious ''peace plan'' for the Mideast gets anywhere for the time being. It is not likely to, Mideast analysts say.

What pleases the Egyptians is that the outside world is not, by and large, pressuring their new President for quick decisions, much less quick results, on Mideast peace.

There is at least the illusion of movement on that front from other quarters - including Saudi Arabia. The spotlight, at least for now, has shifted from Cairo.

The Saudis are not the only ones helping out in this regard.

President Reagan has said some hedgingly nice things about the Saudi plan. In a Time magazine interview released Nov. 2, he also spoke of widening peace efforts to include other Arabs, and of seeking a fair solution to the Palestinian problem.

Jordan's King Hussein, a public opponent of the Camp David accords, was in the US Nov. 2 for talks with Mr. Reagan. The King and other Arab leaders will meet for summit talks in late November.

Palestine Liberation Organization chief Yasser Arafat, meanwhile, says he is taking a ''wait-and-see'' attitude toward Mr. Mubarak, and has, with habitual caution, welcomed the Saudi peace proposals. He says they will be discussed at the Arab summit.

The Soviets, clearly hopeful they will soon be delivering a biting funeral oration for the Camp David process, are also being relatively nice to Mr. Mubarak. They sent him a telegram saying, in effect, they would like to be on friendlier terms with Egypt. The official Soviet media have suggested that the continuity in Cairo policy since Mr. Sadat's assassination owes more to US ''imperialist pressure'' than to Mr. Mubarak, himself.

Israel, for its part, has publicly stressed willingness to work energetically with the new Egyptian president for progress on the long-stalled Palestinian autonomy talks.

Those talks are due to resume here in the second week of November and could, some Cairo analysts believe, begin providing an answer to an important, still open, question here: just how long Mr. Mubarak's diplomatic honeymoon will last.