NOW THAT an extraordinarily broad and effective military alliance is arrayed against Iraq, the next question is who pays for it. President Bush is sending his secretaries of State and Treasury off around the world to pass the hat among the richer allies -- particularly those who most benefit from a steady flow of oil from the Persian Gulf. He is moving quickly to deflect two dangers. First and most obvious, some of the countries that have joined the alliance haven't the financial strength to stay in it unaided for long. Beyond that, he correctly senses a rising resentment here in this country that the United States seems to be paying most of the bills for a military operation to ensure an oil supply on which the Japanese and Europeans are even more dependent than Americans.

Iraq's invasion of Kuwait has not provided any truce in the intense economic competition among the world's industrial powers. Accusations of Japanese and German freeloading are already very audible in this country, and their governments as well as Mr. Bush's administration need to consider it a matter of some urgency to produce a compelling response. Here in Washington the budget negotiations between the administration and the congressional leadership will recommence this week, sharpening the tension between defense and social spending. Mr. Bush cannot let himself be put in the position of pressing for cuts in the social budget to pay for a disproportionate share of the costs of Desert Shield and to protect the prosperity of countries that in many respects are financially stronger than the United States.

The politics of this global collection of contributions to Desert Shield is anything but simple. When other wealthy countries send money, they will touch the longstanding uneasiness here that the United States is allowing its armed forces to be turned into mercenaries, rented out to those who do not care to do their own fighting. Sen. Patrick Leahy (D-Vt.) brought up that concern last week, and President Bush, who responded in his Thursday press conference, is right to take it seriously. He needs to develop his answer more explicitly, but he's making the correct distinction. American troops are in the Saudi desert for American reasons, to protect American interests. But since other countries share those interests, they can reasonably be expected either to send their own forces, as many have done, or to help sustain the costs of keeping troops there.

Mr. Bush speaks of the post-postwar world, in which is is no longer the threat of Soviet tanks that holds alliances together. The structure of this new world will be heavily influenced by the ultimate success -- or lack of it -- of this new alliance against Iraq's aggression. Its military capabilities are formidable. But any alliance needs a firm political base, including clear and fair agreements regarding who contributes what. That's the side of the operation that needs attention now.