Why world bankers scramble to keep poor nations afloat

''People are finally realizing,'' investment banker Felix Rohatyn says, ''that we have become the prisoner of our debtors'' in the third world.

Poor nations of the world have thrown their chains of debt - totaling hundreds of billions of dollars - over the great international banks that have lent them cash.

That cash, of course, belongs to depositors - both individual and corporate - who put their money into banks to earn interest in what were supposed to be safe havens.

It may be right and proper, but in fact too late, to blame the major banks for overlending to countries whose economic prospects were shaky.

The problem has become more fundamental - how to prevent that top-heavy burden of debt from crashing down and wrecking the international banking system.

''The major banks,'' says C. Fred Bergsten, director of the Institute for International Economics in Washington, ''were imprudent. They lent more, always assuming there would be an international bailout, if one or more debtors got into trouble.''

Hundreds of banks already have scrambled to put together rescue packages - lending more money and stretching out debt repayment - to Poland and Mexico.

But other countries stand in the wings, appealing for special help. Altogether, Mr. Bergsten says, developing nations owe an estimated $327 billion to Western commercial banks, plus more than $200 billion to central banks and international lending agencies.

A snap answer might be: ''At least stop throwing good money after bad, until they repay past debts!''

While this logic might be sound for an individual or corporate debtor, almost all experts agree that, willy-nilly, banks have to go on lending to debtor nations.

''Banks can't stop lending now,'' said Mr. Rohatyn Nov. 21 on ''Face the Nation'' (CBS-TV), ''because if they stop lending now, you are going to have some terrible social problems in these (debtor) countries that will force them to the wall politically.''

''Big banks cannot back out precipitously from their loans,'' says Bergsten, a former assistant US Treasury secretary, ''lest they send the debtor country straight into default and lose their loan money.''

The nine largest Americans banks, to cite a part of the problem, have multibillions in loans out to Mexico, Brazil, and Argentina - all on the verge of fiscal failure.

A flood of national defaults could destroy confidence in the banking system, causing thousands of depositors - large and small - to withdraw assets from troubled banks.

Americans sell more manufactured goods to developing nations than they do to Europe and Japan combined. Without a continuing flow of loan capital, the economies of poor nations would dry up. So would their purchases of US goods.

What to do? No one has a simple answer, because the fate of the poor countries and their debts is tied inextricably to the economic well-being of the rich industrial powers.

The latter - embracing the US, Canada, Western Europe, and Japan - are mired in various degrees of recession and high unemployment. Taken as a whole, these powers are unlikely to enjoy brisk economic growth for some time to come.

This spells hardship for developing countries, which depend on selling their traditional exports - commodities, textiles, and increasingly manufactures - to markets in the West. When those markets slump, the debtor nations have no alternative but to borrow more money to finance essential imports.

Pending world recovery, Western banks and their central banks have been coping with the debt burden on a case-by-case basis, with Poland, Mexico, Argentina, and Brazil the most notable examples.

Recently 31 major US, European, and Japanese banks agreed to search for ways to coordinate their international lending, including the sharing of information on debtor lands.

Efforts also are under way to increase the amount of capital available to the International Monetary Fund, with which to bail out crisis cases.

A long-term solution, says Rohatyn, ''is going to require some kind of coordinated action among the US, the Western Europeans, and the Japanese to create an economic environment of much higher growth in the West, to prevent a collapse from happening in the rest of the world.''

The time, he agrees, could hardly be worse for seeking greater world cooperation, when unemployment is driving governments to shield industries from foreign competition.