The United States achieved a major political victory recently when 74 trade ministers from the developed and developing world met in Punta del Este, Uruguay.

The gathering was a direct result of an intense four-year White House effort to get the rest of the free world to accept a U.S. agenda for another multilateral trade round - this would be the eighth - under the auspices of the General Agreement on Tariffs and Trade.The United States achieved its goal. The talks, scheduled to begin late this month, will prominently focus on two key U.S. demands: the establishment of new rules to ensure freer trade in services (insurance, telecommunications, and banking) and major reductions in agricultural export subsidies.

All of this comes as good news for the Reagan administration whose top trade representative, Clayton Yeutter, threatened a walkout even before the meeting began because of last minute wrangles over the agenda. Mr. Yeutter now hails the subsequent agreement as "a major victory for the principles of free and fair trade." It is.

But if the administration is serious about advancing its negotiations agenda once the talks begin in Geneva, it needs to implement an appropriate follow-up strategy for waging what promises to be the most difficult negotiating round in GATT's 40-year history.

These talks could be pivotal. Trade remains the single most important growth catalyst in the world economy. Since 1945, combined exports and imports have grown between 1 percent and 2.5 percent faster than gross national product. In 1984, while trade jumped by a spectacular 9 percent, world GNP expanded by 5 percent.

"The expansion of trade stimulates growth by opening new markets for the exporting country and by freeing resources and stimulating productivity in the importing country. In short, liberal trade represents a supply-side policy for economic growth." Gary Hufbauer and Jeffrey Schott arrived at this conclusion in a 1985 book they wrote for the Institute for International Economics.

But trade growth slackened off recently. And with protectionism again on the rise, the Punta del Este breakthrough came at a most appropriate moment.

The immediate task facing the White House - Mr. Yeutter in particular - is to generate political support for the new trade round beyond the Executive Branch. That's a tall order. And there isn't much time. Failure to establish a larger constituency for these negotiations, however, will virtually guarantee their collapse.

The job begins at home, starting with Congress. The administration needs to recognize that a tough lobbying battle looms if it expects to receive appropriate negotiating authority for the next GATT round from a Democratically controlled House and Senate. Even before the fall elections, congressional support for the administration's trade initiative was tepid.

Of 535 members, the only one to attend the Punta del Este meeting was Rep. William Frenzel, R-Minn., who constitutes one of a small number of GATT- oriented free traders in Congress. But the new Congress may if anything be even less enthusiastic.

Not surprisingly, Mr. Frenzel, a member of the Ways and Means Trade Subcommittee, is upbeat. "The agenda of Punta del Este constitutes a splendid beginning," he says. But a staffer who works closely with the Senate Finance Committee may express the dominant congressional view. "If these talks get off the ground, we might be prepared to take them seriously - in two or three years,"

That's too much time. Given the skepticism of the new Congress, the administration must push hard over the next six months for a tangible breakthrough if it expects to retain Republican support for the initiative while winning over large numbers of Democrats.

One possibility: a firm indication from the Brazils and Indias of this world that they are seriously prepared to negotiate with the West on abandoning hothouse protection of their service industries. They agreed to do as much at Punta del Este.

The White House also needs to firm up international support for the forthcoming negotiations, beginning with our Japanese and European Community allies. Don't be misled by the glowing reports of Allied solidarity with the United States on this issue.

Up to now, Tokyo and Brussels have accepted the new trade round as a ''favor to Uncle Sam," forced on them by an administration which hopes to use the new talks to diffuse protectionism in Congress - not as an opportunity to improve the functioning of the global trade system from which they also benefit.

"The reality is that Tokyo and Brussels are perfectly happy with the present system of trade rules which they have been able to bend to their advantage. It's the United States which is the odd man out," explains Alan Stoga, senior associate at Kissinger Associates Inc.

Japanese and European parochialism is hardly new. With respect to the forthcoming GATT round, however, the Reagan administration needs to convince Japan and Europe that their own oxen could end up being gored if the world moves headlong into protectionism, and the subsequent closing off of markets which participants in the new round are ostensibly pledged to prevent.

In the meantime, the United States should start negotiating with more enthusiastic players. For example, take the so-called Group of 14, or "Fair Trade" countries with whom we teamed up at Punta del Este in a successful effort to force the European Community to accept a call for phased reductions in farm subsidies.

Similar help can be expected from a growing number of advanced Third World countries that, thanks to U.S. pressure, now recognize that their own economic fortunes also hinge on a successful trade round. One such country is South Korea.

A source close to Mr. Yeutter gives Seoul high marks for its energetic lobbying on behalf of the forthcoming GATT negotiations. "The Koreans ended up taking a lot of flack from militant Third World countries for doing so," he says. More Koreas, please.

U.S. profits and employment increasingly depend on the ability of U.S. firms successfully to compete in the global marketplace. By enabling us to revise the world's trade rules, the new GATT round affords the United States a key opportunity to do just that. This then is a worthy bipartisan agenda which both the White House and Congress would be well advised to pursue.

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