TANZANIA RENDERED what it and a great many other countries, including the United States, thought was a major international service by helping oust Idi Amin from Uganda earlier this year. Yet the war did grievous damage to Tanzania's frail civilian economy, tearing up the northern part of the country where part of the war was fought and inflicting dislocations throughout the whole structure. These costs, added to Tanzania's already great economic difficulties, have virtually crippled the country and forced it to ask nine of its regular aid donors in the industrialized world to provide a quick $375 million to stave off a complete collapse. Justice and a proper appreciation of Tanzania's service compel a generous response, but the response so far has been slight.

Now, though the war put Tanzania in the hole, Tanzania is not asking its friends to finance the war. It has identified legitimate civilian projects. Yet none of the donor countries likes to offer budgetary or balance-of-payments support - cash right now - which is what Tanzania most needs. It needs it to finance the imports that will allow it to produce the exports that will enable it to earn the foreign exchange in the absence of which it need the special aid: truly a vicious circle. The donors prefer to support real development projects, and they are reluctant to shift funds from development to budgetary support, though some may decide to do so.

Tanzania, of course, is not the only country with a strong claim on American favor. What about Uganda itself? The United States is turning out its pockets fof a few odd dollars, but there are limits: It is the end of one fiscal year, the request came too late to get into the current aid budget, and there are no contingency funds to speak of. Food aid is one possibility. Tanzania could yet go to the International Monetary Fund, which has already provided two credits totalling $50 million this year, but additional credits would require it to submit to additional conditions. The Tanzanians regard these as so severe that they wish to exhaust their quest for unconditional money first.

But, you may say, since Tanzania is prominent in Third World circles, why does it not go to the money men of the Third World, OPEC's Arabs? Alas, Idi Amin was a Moslem and conducted both an internal policy and a foreign policy centered on a Moslem strategy. That leaves the considerable burden of Tanzania's distress on - after its citizens - its friends elsewhere in the world.