Domenico Minchilli, the Italian architect who designed Mr. Ben Chorin's house, said, ''I advise my Italian clients to put them in.'' He attributed the trend less to midges than to modernity. ''It's like the locals buying a washing machine, while they used to do their wash at the village tub.''

In France, Mr. Del Vecchio said, a geographical divide exists, so that screens are sometimes found in homes and commercial buildings in the south, though rarely in the north. Even so, he estimates that in Provence, the region of France where screens are most widely used, fewer than one in four homes have them. In Britain, Mr. Hay said, no market studies exist, but he puts the figure at fewer than 5 percent. Most customers are commercial -- hospitals, offices, factories, stores.

American visitors who have spent an evening at a sidewalk cafe in Paris or Rome will have noticed that far less energy is spent swatting bugs than in, say, Boston or Philadelphia. Yet that does not mean Europe does not have its insects.

''In general, there is probably as much diversity in Europe as there is in North America,'' said Michel Martinez, an entomologist at the National Institute for Agricultural Research, in Montpellier, France. Yet while some regions of Europe, like Scandinavia with its many lakes, abound in bugs, others appear to be almost bug-free.

Nevertheless, experts have observed troubling changes in the bug population over all, Mr. Martinez said, as environmental pollution decimates some species while rising temperatures lure tougher mosquitoes and other bugs from northern Africa to Europe's Mediterranean rim. That in turn drives indigenous bugs further north, a development the screen makers can only welcome.

American screen manufacturers have not entered the European market. The American industry, said Linda Costain, the customer service manager at E. J. Kidd & Company, a big regional screen maker in Raleigh, N.C., is largely local because of the difficulty of shipping screens; the thin frames and mesh make them relatively fragile. Would Kidd be interested in Europe? ''I think we would,'' she said, ''if we could figure out a way to get them over there without getting them damaged.''

In part, Europe's familiarity with screens came from American expatriates who, finding none readily available, simply built their own.