LAST WEEK'S DRAMATIC BREAKTHROUGH in the Bosnia peace talks certainly stirred cheers in Europe--and a sigh of relief that a running sore in transatlantic relations may finally start to heal. Uncle Sam wanted to stay out of the morass. Only after Europe's humiliating failure to stop the bloodshed did the U.S. reluctantly step in to clean up the mess, and then primarily to answer domestic critics. Yet the sense of relief has an edge of anxiety to it: Congress's reluctance to support President Clinton's promise of troops to police the accord has raised fears that the U.S. may yet renege on its traditional commitment to European security.

The bad blood over the Balkans is only the most visible sign of a broader post-cold war malaise felt by the Old World over its ties to the New. The number of American troops in Europe, the most important and visible measure of how much Washington really cares, has been slashed by two-thirds, to just 100,000, and some influential U.S. analysts believe it should be cut to zero now that Europe faces no external threat.

Economically, too, Europe is feeling hard done by. While the Continent has struggled with recession, unemployment and burdensome welfare systems, America came roaring back in the '90s, helped by a more competitive dollar, leaping over Europe's smokestacks with hot new computer and software technologies. The value of U.S. trade is 50% higher with Pacific nations than with its Atlantic partners, and the Clinton Administration came into office openly romancing dynamic Asia. The Commerce Department is targeting big emerging markets around the globe, everywhere but Europe.

A big shock for Europeans was the 1994 election that swept into Congress a breed of neoisolationist Republicans. "We see an America looking inward with plenty to keep it occupied at home," says Gebhard Schweigler of Germany's Research Institute for International Policy and Security. "That worries us." European leaders have taken up the cry that the U.S. and Europe are drifting apart. "The glue which kept us together has lost its strength," warns Belgium's Prime Minister, Jean-Luc Dehaene, using a favorite European metaphor. German Chancellor Helmut Kohl voices similar concerns, and British Foreign Secretary Malcolm Rifkind has made "renewal" of the relationship a "top priority."

But hold on. The drift may be more perception than reality. Europe's rich countries remain a huge market for American exports. Adding sales on both sides of the Atlantic by U.S.- and European-owned affiliates to trade figures brings total transatlantic commerce to $1.7 trillion, vs. $1.1 trillion across the Pacific.

The U.S. has committed itself not only to keeping NATO but also to expanding it to give the alliance new purpose. And nothing will change the fact that the two sides share common values and heritage. Still, warns America's European Union ambassador, Stuart Eizenstat, "perception can become reality." Policymakers worry that European uncertainty may lead to anti-Americanism by amplifying the drumbeat of daily irritants--disputes ranging from current U.S. protests over E.U. quotas against American banana marketers to the Hollywood-movie invasion of the Continent.

To stop the bickering, a Big Idea in politicians' parlance, President Clinton and E.U. leaders will meet this weekend in Madrid to sign a New Transatlantic Agenda, a sweeping document that along with a companion action plan pledges cooperation in areas ranging from trade to drug enforcement. Some officials in Germany, Britain and other northern E.U. countries believe the next major goal of the alliance should be to form a Transatlantic Free Trade Area (TAFTA). But the U.S. has been cool to plunging ahead, arguing it is too soon after the bruising domestic fights over the North American Free Trade Agreement and the Uruguay Round trade pact, which set up the World Trade Organization. And for France and other Southern European countries fearing for their highly protected farmers, free trade is taboo. Nevertheless, last week, in a surprise compromise, the E.U. agreed to a joint study on a new transatlantic marketplace that would cut or eliminate tariff and nontariff barriers, without mentioning the "F word."

This commitment to move toward freer trade will be the centerpiece of the sprawling action plan that underpins the Transatlantic Agenda's lofty principles, with more than 100 ideas to foster E.U.-U.S. coordination. Both sides will vow to speed up already-agreed-upon tariff cuts; negotiate an information technology accord; sign a new customs-cooperation deal by the end of 1996; create a high-level group to coordinate foreign aid; launch a "no place to hide" initiative to combat organized crime and narcotics; cooperate more closely in the Middle East, including opening markets to the Palestinians; and bring the E.U. into the North Korean nuclear antiproliferation effort. "This is the biggest step forward in E.U.-U.S relations since the European Community was founded," claims Eizenstat.

Skeptics may cavil. The 1990 Transatlantic Declaration proved a hollow exercise, largely because it lacked specifics. Now comes the promise of "high-level" follow-up. In a relationship dogged more by neglect than rancor, this may well be the second honeymoon that rekindles the romance.

--With reporting by Barry Hillenbrand/London and Bruce van Voorst/Bonn