Coca-Cola Co. last month had a question for the U.S. military: Would the troops in Saudi Arabia like 20,000 cases of Coke stored in a warehouse there? Certainly, field commanders said. So, with an armed escort, the company trucked 2,000 cases a day across torrid desert roads to forward base camps. Watching sweaty GIs unload the free drinks, company employees "felt like Santa Claus," said Randy Donaldson, a Coca-Cola spokesman.

A woman from New Brunswick, Maine, got a less enthusiastic response when she called the Defense Logistics Agency to offer the troops 2,000 to 3,000 lobsters, packed in ice. Officials dutifully referred her idea up through channels. But few expected it would be accepted, due to the cost of shipping, handling and storing food of that quality.

These are only two of a rash of proposals the military has been fielding in recent weeks from individuals and companies who want to do something special for the troops, on their own dime. Among the offerings: a cache of Haagen-Dazs ice cream, 100 head of cattle, umbrellas (undoubtedly to shield against the desert sun), 500 copies a week of Time magazine and videocassette recorders. A plumber called to offer to fly to the gulf to apply his skills. So did an air-conditioning technician.

Many donors have been turned down, because of lack of need, prohibitive costs of handling the gift or old-fashioned military bureaucracy. Others, however, have managed to get welcomed items into the hands of soldiers far from home. More is on the way, as the privately funded recreation agency USO, the traditional conduit for such gifts, prepares to set up in the region later this month.

Companies view donations as patriotic and civic duty and, of course, get positive publicity from it. Individuals' motives tend to be more single-minded. "They've seen what it's like over there on the news and they want to do something to help the troops out," said Paul Trkula, a logistics agency official who oversees a hot line (703-274-3561) set up to field would-be donors' calls.

Early in the crisis, the calls coming into the agency's offices in Alexandria focused on drinking water. People had seen TV images of the troops upending bottle after bottle in the desert heat and feared a shortage. In fact, said Pat Miller, an agency spokeswoman, there was plenty of water, and this and many subsequent offers had to be politely declined. "Patriotism is patriotism and people want to support the troops," she said. "But they do have everything they need."

When the crisis broke out, the General Services Administration empowered the logistics agency to accept donations under a 1954 law that had been used mainly for accepting such things as works of art. Still, the government is not entirely at ease with the idea of donations. Accepting gifts requires its own set of procedures and can complicate the military supply system.

Food may spoil en route. Picking up small shipments of the supplies, sending them to the gulf, tracking them and distributing them may be prohibitively expensive. Moreover, noted Miller, contractors may complain. "Let's say someone does donate sunscreen. This would take business away from people who would normally be selling us sunscreen. And then you'd have a complaint. ... It's very hard to make everyone happy," he said.

The agency is now looking favorably on proposals to donate such drinks as Gatorade. And it will probably approve a request from a California high school to ship 1,000 one-pound "care packages" to the region. The Pentagon is open to the idea of cash donations, too. A church group in Detroit recently called to offer $10,000.

More goods will flow once the USO gets into the region. It is preparing to set up hospitality centers and live entertainment at bases in Saudi Arabia, Turkey and Egypt and aboard U.S. ships in the region. Its gulf effort is being helped by Coca-Cola, Anheuser-Busch Inc., American Telephone & Telegraph Co. and American International Group Inc., an insurance company. Each pledged $500,000 after the crisis erupted.

Among the hand-outs that it plans: music cassettes recorded by a Washington area radio station, WAVA, and about 60 other U.S. stations, and "oasis packages" that will include cheese products donated by Kraft Inc.

A Las Vegas hotel and casino company, Circus Circus Enterprises Inc., has meanwhile done its part to combat the boredom of military duty by donating 10,000 decks of playing cards. A retired Air Force sergeant set up the deal; the cards were quickly loaded aboard an Air Force plane and flown out. In the military "there's a lot of poker played but there's also a lot of crap games," said company executive vice president Mel Larson. "... The next thing we're trying to do is round up 500 pairs of dice for them."

US Sprint Communications Co. has set up a toll-free number at which people can request facsimile-machine-delivered news reports on developments in the gulf (1-800-676-2255). The long-distance telephone company has also handled emergency calls relayed by amateur radio operators in the region.