THEIR EXCHANGE OF ambassadors brings relations between Egypt and Israel into a state of normality for the first time since Israel was established in 1948. What problems they have -- and they will have more than their share -- will now be addressed face-to-face on the basis of mutual respect: the best way of doing international business. It was just a few years ago that, to make their points to each other, the two might launch all-out war.

It is nearly a year since the signing of the Camp David peace treaty, from which this exchange of envoys and much else have flowed. For both Egypt and Israel it has meant the forging of peace -- this is the great feat -- but it has meant too a quiet, intense competition for American favor. Mainly this is the result of Egypt's coming in from the geopolitical wilderness. After 1973, Cairo had no solid great-power connection, but Camp David let it join Israel as a petitioner for ever-creasing amounts of American economic and military aid -- and for a role as co-holder of the American strategic franchise in the region.

Certainly the two countries are entitled to the comforts of military power. It does seem a bit strange, however, that the more the principal threat (from the other) to each of them is reduced, and the more desperate the plight of their respective civilian economies becomes, the more arms (on the cuff) they ask. Israel at least has certain cold rationale: as long as it plants settlements in the West Bank and suppresses Palestinian nationalism there, it must prepare militarily for the worst. It must, for instance, prudently anticipate a post-Sadat policy reversal; hence it lobbies now, awkwardly, to limit the flow of high-technology American arms to Cario. Meanwhile, Egypt under Anwar Sadat does not so much have significant military foes as large military ambitions. The Americans, continually pressed to prove their own point that peace pays, have a hard time telling him no.

No matter how his critics charge him with betrayal, Anwar Sadat has never stopped endorsing the cause of Palestinian nationalism, one of the endemic causes of political instability in the region. Menachem Begin has never started to endorse it. Mr. Sadat has been uniformly, even devoutly, faithful to the Camp David accords in their Palestinian aspect, as in others. The United States has no quarrel with him on his question. But Mr. Begin, though he has shown courage in dealing with Egypt, has got himself a large quarrel brewing with the United States on the Palestinians and, with the Camp David emphasis now swinging from Egyptian-Israeli ties to Palestinian autonomy, it will become increasingly evident. By sending an ambassador to Jerusalem (actually, to Tel Aviv), Egypt establishes yet further credit in Washington. By sending an ambassador to Cario, Israel assures itself a confrontation with the United States.