A recent issue of October magazine, the Cairo weekly now serializing the memoirs of President Anwar Sadat, carries an account of his dealings with the Nazis in World War II. "Hitler exhilarated me," Sadat says in the memoirs. "I can't find words to describe the admiration I felt for German militarism."

Shocking as that may seem to most Westerners, and especially Jews and Israelis, it is no more shocking than the past of Israel's prime minister, Meanhem Begin, seems to most Arabs. In their eyes, Begin is a hard-line terrorist who stopped at nothing, including the murder of Arab children, to achieve Israeli aims. "He is," Mohammed Sid Ahmed of the newspaper Al Ahram said to me, "a Jewish fascist."

The fact is that both present leaders of Egypt and Israel are right wing nationalists. Ideological harmony fostered their original affinity. Sadat, in an interview the other day, told me he had no prejudices against Begin from the moment he became leader of Israel last May.

The first stage of the Cairo conference now under way here is chiefly designed to institutionalize the personal connection for further diplomatic action. If the first stage succeeds, which seems almost certain, what then shapes up is a peace of the hawks - with all the strong points and limitations that implies.

One strong point is familiar. Peace inevitably entails compromise of national objectives. Doves, well known as favorable to concessions, are vulnerable to political attack on nationalistic grounds. So they find it well-nigh impossible to build the domestic support necessary for compromise settlements.

Hawks, with tough-guy credentials, in contrast, are proof against attack from the nationalists. That is why Gen. Charles de Gaulle could make peace with the Algerians when the French Socialists could not, and why President Nixon could make the opening to China that eluded the Democrats.

Great power implications, apparently difficult for many people to grasp, also go with the peace of the hawks. President Sadat is allergic to the Russians, and he loses no opportunity to bait the bear. It is typical thathe unilaterally expelled most Russians from Egypt in 1972. Equally that he blames them for Syrian Iraqi and Palestinian opposition to hsi dramatic peace initiative. Aso that he invited the Russians to the Cairo conference in terms they were bound to reject.

Prime Minister Begin is every bit as anti-Communist. He has never forgotten the time he served in Russian prison camps during World War II. Only the other day in a parliamentary debate he showed his scorn for the term "Palestinian" by referring to it as not a Hebrew but a "Soviet" word.

Any settlement that emerges between Sadat and Begin is bound to diminist even further the Soviet role in the Middle East. It will also be hard on those who played with Moscow - notably the Syrians and the Palestine Liberation Organization.

Washington's interest in these conditions is not to try to deal Russia into a comprehensive solution for the Middle East, nor to run after the PLO and the Syrians. It is to limit the damage that an anti-Soviet settlement in the Middle East might do to negotiations between the United States and the Soviet Union on arms control. In the bargain, a pro-Western settlement in the Middle East might be used to help President Cart in the Congress, which suspects him of being too prone to making concessions to the Communists and their friends on such matters as Panama and arms control.

The peace of the hawks, finally, implies exclusion of the local parties and leaders most imbued with humanitarian concern for internal problems of social welfare. Military men on both sides are playing a bit role in the engotiations - not trade-union leaders or teconomic planners or population experts or agronomists or even persons with visions of a better life. It can be expected that the miserable conditions that presently prevail, especially in Egypt, will survive whatever agreements are reached.

At best, in other words, the settlement shaping up will be decidedly limited. International rivalries will ben ot ended, but localized - and to the temporary disadvantage of the Communists. Underlying social problems will be not solved, but prolonged - to the advantage of those who would exploit them.

So it is important not to oversell what is happening here with talkof a "golden age" for Israel or an "Arab renaissance." The peace of the hawks is the best that is possible - but that is not very good.