The two superpowers have lost no time in trying to influence the policies of post-Sadat Egypt to their advantage. The United States appears determined to prevent any vacuum in the Nile Valley in the wake of President Sadat's assassination. It has moved quickly to announce that US military aid to Egypt and Sudan is to be stepped up; that US military missions are already visiting both countries; and that joint US-Egypt military exercises planned to take place in the desert outside Cairo next month are to be expanded.
The immediate aim of the US moves is to beef up Egyptian and Sudanese defenses against my threat from Libyan leader Muammar Qaddafi to the west -- and through him from the USSR.
But beyond that, the US probably hopes to show other Arab lands that it can at least deliver on an Egyptian-Sudanese request for help -- even if it has been able to deliver on the question of the Palestinians and is faced with possible defeat on its effort to supply AWACS surveillance planes to Saudi Arabia.
The Soviet Union, with its latest warnings and official protests against US interference in Egypt and against expansion of the US military presence in the Mideast, probably has three main aims:
* To block any strengthening of the US military and political presence in the Middle East in response to the requests of the fledgling Mubarak regime in Egypt for American support.
* To pry open the door for a Soviet return to the Middle East peacemaking process, from which the Russians have been excluded since President Sadat made his dramatic visit to Jerusalem in 1977. (Russian czars and commissars alike have always seen the Middle East as their strategic backdoor.)
* To repay the Americans for the embarrassment caused the USSR by constant and blunt warnings from President Reagan and Secretary of State Alexander M. Haig Jr. against Soviet interference in the internal affairs of Poland.
One sentence in the Soviet "statement to the government of the US" is particularly significant and indicates that the declaration is no mere propaganda move. That sentence reads: "What is happening around Egypt cannot but affect the interests of the Soviet Union's security, and it will attentively follow the development of events."
Also of significance are the facts that the Soviets summoned the US charge d'affairs to the Foreign Ministry to give him the warning in person and that it was addressed to Washington alone. There is not even a hint of protest or rebuke to Egypttian President-designate Hosni Mubarak.
Implicit in this is Moscow's leaving of the door open for Mr. Mubarak to veer away in due course from Mr. Sadat's near-total commitment to the US and toward a friendlier relationship with the Soviet Union. In other words, the Russians appear to be handling Mr. Mubarak with kid gloves, in contrast to their chill attitude toward Mr. Sadat, to whose funeral they sent no special representative.
Mr. Haig headed the high-powered special US delegation which flew to Cairo for the Sadat funeral. He stayed on after the ceremonies and used the occasion for a round of earnest diplomatic activities -- not only with Mr. Mubarak and other top Egyptian officials but also with such key heads of government attending the funeral as Israeli Prime Minister Menachim Begin and Sudanese President Jaafar Nimeiry.
There are signs that the US may be putting pressure on Israel to play its part by making moves of its own aimed at helping President-designate Mubarak as he seeks to establish himself and take control of an Egypt without Sadat.
In a television interview taped just before leaving for Cairo and aired at the weekend, Mr. Haig said that the Reagan administration hoped "there would not be a further enlarging of West Bank settlements" in territory occupied by Israel since the 1967 Arab-Israel war. There had been reports last week that Israel was about to expand these settlements further -- an obvious embarrassment to Mr. Mubarak's team negotiating on Palestinian autonomy.
Further, after his talk with Mr. Mubarak, Mr. Haid described Egypt as America's "foremost" friend in the Middle East, a formulation that will not be lost on Israel and could cause irritation there. According to some reports Mr. Haig, during his talk with Mr. Begin in Cairo, not only raised the question of West Bank settlements but also mentioned the possibility of Israel's helping Mr. Mubarak by expediting the final withdrawal of Israeli troops the Sinai by April 1982.
As for his talks with Sudanese President Nimeiry, Mr. Haig will have had an opportunity to explain to the latter -- who has both economic and political problems at home -- how far the US will go to help Sudan face any threat from Libyan troops across the border in Chad. Libyan planes have been bombing Sudanese border villages to prevent anti-Libyan Chadian guerrillas from using them as sanctuaries.
Newsweek magazine reports that the US and Sudan are considering a joint military commission to draw up contingency plans on how to deal with any major Libyan attack on Sudan. The magazine also says that in coming military exercises, US troops would join in airlifting Egyptian troops to Sudan as part of the maneuvers.