Already, some companies are warning of lower earnings. Tate & Lyle, the British maker of Splenda sweetener, angered shareholders after saying that a drop in the dollar would hit second-half pretax profits. And Europe's largest papermakers, Stora Enso and UPM-Kymmene of Finland, took a hit after Deutsche Bank downgraded their stocks to ''sell,'' saying that the weak dollar would crimp their export volumes.

European stock prices have so far remained buoyant, but a recent survey found that investor confidence in the euro nations had sunk to its lowest level in two years.

The combination of a weak dollar and a slowing U.S. economy ''is kind of a double whammy for some European export companies,'' says Kurt Umbarger, portfolio specialist for international equities at T. Rowe Price. ''The Unilevers of the world, we just don’t own.''

Yet it is not as simple as that. Many European companies sell goods in nondollar markets overseas. Those that are heavily involved in emerging markets will probably do well, as will those whose main market is still Europe.

Atlas Copco, a Swedish mining-equipment company active in emerging markets, has such strong demand for its products that it ''will more than compensate for any currency headwind [it] will face,'' says Umbarger. Another Swedish company, H&M, has actually benefited from the weak-dollar trend because the majority of the clothing retailer’s goods are made in Asia, where many currencies closely track the dollar.

Even companies dependent on the U.S. market have been able to soften the blow by hedging some of their exposure to currency risk through financial derivatives (which is only a short-term solution), and by diversifying where they buy their raw materials and where they construct their products. Both LM Ericsson of Sweden and EADS use currency hedges. Many foreign manufacturers, including Volkswagen and BMW, use ''natural hedges'' as well. BMW, for instance, has plants in both the United States—its largest export market—and in China. It plans to increase production in both countries.

And even though some big European companies will take hits, Europe is less dependent on the American market than it once was.

''The whole world is less sensitive to the U.S., so the impact of the dollar is less pronounced,” explains S.&P.'s international equity strategist, Alec Young, predicting that the persistent strength in the euro is only ''a moderate headwind for European sales and earnings.''