THE REAGAN administration's advice to the developing countries is to put their faith mainly in private investment and free trade. The administration's evolving policies toward the poor countries seem, happily, to be less hostile to international aid than the original rhetoric suggested. But the generosity is clearly going to be limited.

Secretary of State Alexander Haig took the high road at the United Nations on Monday when he acknowledged both the value of the multilateral development banks and this country's responsibility to continue supporting them. But, simultaneously, Treasury Secretary Donald Regan took a slightly less elevated tone in his press conference, where he sharply emphasized that the United States does not want those operations expanded.

It's a compromise, and it owes a good deal to Mr. Haig's understanding of the intolerable political price of a crabbed and greedy retreat from the principle of aid on the part of the world's richest nation. The United Nations' General Assembly has opened, bringing the foreign ministers of most of the world's governments to New York. Next week there will be the annual meetings of the World Bank and the International Monetary Fund, bringing the finance and economics ministers to Washington. Next month President Reagan will go to Mexico for the meetings of the rich and poor countries at Cancun. Secretaries Haig and Regan are delivering the message that the president does not intend to threaten the present structure of support--but neither is he going to assist in any exotic departures like export price supports.

What's the prospect for the countries with the low incomes and high death rates as they struggle to raise their people's standards of living? Cash aid certainly isn't going to increase. As for commercial credit, most of the big international banks have already made enormous loans to the Third World and are uneasy about any further rapid expansion. That leaves trade.

"The industrialized countries have a special responsibility to work for a more open trading system with improved rules," Secretary Haig said at the United Nations. He's entirely right. Meanwhile, you will want to know, negotiators from the United States and other countries are meeting in Geneva to work out the next phase of something called the Multi-Fiber Agreement. It sets the quotas for imports of textiles into the rich industrial countries. Textiles provide an outstanding opportunity for a country in the early stages of industrialization to raise its income--if it can sell its goods. Most of the European governments are pressing fiercely for smaller quotas, to protect their own industries. Mr. Reagan will doubtless be hearing from the textile states, and from their Republican senators. Will he go along with them and the restrictive quotas that they want? Or will he defend the principle of free trade? That will be a fair test of the administration's determination to stand by its fair words at the United Nations.