Israel and Egypt, which are still very much at odds over many issues, have found an unusual common cause -- a military debt burden that is forcing them to use most of the economic aid they receive from the United States to make payments on previous U.S. arms purchases.

The two countries are stark illustrations of a trend in the flow of assistance between Washington and several of its most important friends, including Turkey, Spain and Thailand. Their military debt is swallowing up their economic assistance.

Both Israel and Egypt, the two largest recipients of U.S. economic and military aid, have brought the issue to a head by pleading with Washington for supplemental aid. Israel is seeking $1.5 billion over two years, and Egypt, $870 million for this year alone.

Egyptian President Hosni Mubarak took up the painful paradox with President Reagan when they met in the White House on March 13. He told The Washington Post the same day that he had told the president that Egypt would pay $560 million next year just to service its $4.5 billion military debt to Washington.

U.S. economic aid, he noted, was running about $800 million a year, leaving Egypt with only $240 million that it could devote to other purposes.

Egypt will pay $10.6 billion for $4.5 billion worth of American arms before it's finished, according to Agency for International Development calculations, and up to $700 million in fiscal 1994 to service its military debt.

Egypt already is more than $225 million behind in its repayments this year and is straining to avoid a congressional dictate that aid must cease if a country falls more than one year in arrears.

Israel, meanwhile, is in even worse shape and is involved in long, hard bargaining with administration officials to convince them that it is worthy of an additional $1.5 billion in aid to see it through its current economic crisis.

The annual payments on the $24 billion it owes foreign countries now run about $4 billion a year. About $1 billion of that goes to service its $10 billion debt to the U.S. government, almost all of which went for arms purchases.

In fact, the bulk of Israel's foreign debt, according to the American-Israel Public Affairs Committee (AIPAC), represents military expenditures. Israel spends about a quarter of its gross national product on defense -- the biggest share of any country in the world.

"Truthfully, the greatest part of the economic aid being requested will never leave the U.S. Treasury because it will, in effect, return as interest and principal payments on past loans," AIPAC executive director Thomas A. Dine told the Senate Foreign Relations Committee March 21.

Israel is slated for $1.2 billion in economic aid this year, but must pay back $1 billion.

Because of an amendment sponsored by Sen. Alan Cranston (D-Calif.) and first applied in 1984, Israel is assured of receiving at least as much economic aid as the amount it owes the United States.

But the U.S. government has come to recognize the absurdity of the situation facing many of its aid recipients. Starting this fiscal year, all military and economic aid to Israel and Egypt is in the form of direct grants rather than loans for arms purchases.

This will take care of the future but still leaves billions of dollars in old debts to pay off. Administration officials say there is only one way to solve that problem -- a special appropriation to cover the debts. But so far, no such legislation has been proposed by either the administration or Congress.