About six months ago, the Airport Hilton Hotel in Burbank, Calif., opened one full floor of rooms for nonsmokers, committing 35 rooms -- out of 277 -- to a smoke-free stay. Guests had been asking for nonsmoking rooms, but management was uncertain whether it would be able to rent them regularly.

"We were a bit apprehensive the first time around," says general manager Richard G. Messer. His fears, as it turns out, were groundless. Because of the popularity of the initial nonsmoking floor, the hotel has just opened a second floor with another 35 rooms. "Now we are delighted because our guests seem to be delighted, and that's what the hotel business is all about."

Similarly, the 686-room Hotel Inter-Continental in New York introduced a nonsmoking floor in what it termed "a cautious test." The 60 rooms on that floor sold out the first night, and at least through the end of May they had filled up every night thereafter. As a result, another nonsmoking floor will be opened this fall.

Health-conscious Americans across the country are strengthening their demands for smoke-free breathing space, and the hotel industry appears to have taken heed. Increasingly, hotels and motels are setting aside rooms, or better yet, entire floors for nonsmokers. In Dallas, the five-year-old Non-Smokers Inn, a 135-room business hotel, is off-limits entirely to smokers.

However, many travelers do not seem to be aware that smoke-free rooms are available, say hotel spokesmen. "Few callers actually initiate a request for a no-smoking room," says Melanie Illian of the New York Inter-Continental. "But when the hotel's reservationists ask, the overwhelming preference is the no-smoking floor."

From the point of view of nonsmokers, the response seems entirely understandable. As Illian acknowledges, one sniff in a standard hotel room can tell you if a chain-smoker occupied it the night before. Nonsmoking rooms are available as singles, doubles and suites.

The American Hotel & Motel Association has not surveyed its members to determine how many offer smoke-free rooms, but spokesman Steve Trombetti says the numbers are growing. One reason is public concern about the hazards of smoking and second-hand smoke. Another is "competition. A hotel doesn't want not to have an amenity" that other hotels offer.

Some of the large hotel chains have made it a corporate policy to provide no-smoking rooms, while others leave the matter up to individual managers.

For example, since about mid-1985, all 84 Hyatt hotels in the United States, Canada and the Caribbean have had either non-smoking rooms or floors, says spokeswoman Carrie Reckert. The minimum is 5 percent of the rooms in each hotel, but many properties have set aside more because of a demand.

The 271 Hiltons in the United States also reserve at least 5 percent of the rooms in each hotel for nonsmokers, according to spokeswoman Barbara Sofie. At the Burbank Airport Hilton, the figure is now 25 percent.

The American Lung Association in New York has put together a list of a dozen or more hotel and motel chains that provide nonsmoking rooms (from 5 to 30 percent) in each property. They include Quality Inns, Days Inns, Embassy Suites and La Quinta Inns. The 850 Quality Inns (which include Comfort Inns and Clarion Hotels and Resorts) donate $2 to the American Lung Association for each reservation received over a special toll-free number, (800) 228-LUNG.

At least 53 of Sheraton's 380 hotels in this country have smoke-free rooms, and they now are an amenity in every new Sheraton that opens, says spokeswoman Susan Kent. Three of the 55 have nonsmoking floors.

In Washington, the new Sheraton Grand on Capitol Hill has two nonsmoking floors. In the past two months, the 1,500-room Sheraton-Washington Hotel has opened 75 nonsmoking rooms (grouped on three floors). So far the demand for them has been good, says spokeswoman Penny Cummings, particularly among medical groups booked for conventions.

With Marriott, the availability of smoke-free rooms "depends on local market conditions," says spokeswoman June Farrell. "Many do have them, but it's not across the board."

For conscientious hotels, converting a room to nonsmoking can be expensive. "We don't just put up a sign on the door," says Cummings of the Washington-Sheraton. Some, like the Inter-Continental and the Washington-Sheraton, introduce them as a part of a general renovation program when the rooms are going to be refurbished anyway.

The Inter-Continental's new nonsmoking floor is one of six that have just been renovated. The second floor will be part of the final fix-up phase. The rooms have to be "deep-cleaned to get the smoke out," says Illian. That means cleaning carpets, wall coverings, drapes and bed linens and replacing some furniture pieces that many have been damaged by cigarette burns.

The hotel, she says, hopes "to ensure that no vestiges of smoke are discernable."

As yet, the Inter-Continental hasn't determined if it's cheaper to maintain a nonsmoking room. But the staff seems to find them more agreeable to clean. "I'm a former smoker," says Illian, "and I've often thought after I leave a full ashtray how unpleasant it must be for them."

Lyndon Sanders, who owns the Non-Smokers Inn in Dallas, figures his staff can clean a nonsmoking room about 26 percent faster than in a similar room where smoking is permitted. Partly because of the savings realized from reduced wear and damage, he says, the hotel has not raised its rates since 1982. A room for two ranges from $32 to $38 a night.

Almost every major hotel chain in the nation has come to him for advice, he says, on how to introduce and manage nonsmoking rooms and floors. The brand new 212-room Truckee River Lodging House in downtown Reno, which had considered going half-smoking and half-nonsmoking when it opened in February, decided to go fully nonsmoking after seeing Sander's example.

Though he maintains he is not a militant antismoker, Sanders, 58, blames the death of his father on cigarette smoking. "It killed him before he was 50. I hated cigarettes."

Before opening his new inn, he had owned a small chain of motels where he provided some nonsmoking rooms. The idea came to him while flying, he says. He saw how much airline passengers appreciated being given a choice of seating in a smoking or nonsmoking section and concluded his guests should have a similar choice in rooms.

Some people doubted an entire smoke-free hotel could be a success, he says, "but we started making a profit before the end of six weeks."

Sanders hires only nonsmokers, and he asks guests to sign a statement agreeing to pay a $250 room-cleaning fee if they smoke in a room. His staff, he says, can tell if someone has smoked in the room. Other guests, who have sought out the smoke-free environment, are quick to chastise anyone who lights up in the hallways or restaurant. So far, only six people have been charged the extra cleaning fee.

In keeping with the spirit of the hotel, Sanders recently renamed the $56-a-night "Governor's Suite." It is now the "Surgeon General's Suite."

What is a smoke-free room?

It should be (although there's no guarantee) a room that either is new or has been thoroughly scrubbed from top to bottom. When Quality Inn first designated nonsmoking rooms, it spent $1 million nationwide to refurbish 10 percent of the rooms in each property, says spokeswoman Susan B. Dynerman. As of January, 15 percent of the rooms have been reserved as smoke-free.

Nonsmoking rooms also should always be off-limits to smokers, even if it is the only vacancy available. Again, there is no guarantee of this. However, some hotels, including Quality Inn, say they will never check a smoker into a nonsmoking room. Says Dynerman: "We haven't run into the problem. They're the rooms that go first."

One judge of a hotel's commitment is the absence of ashtrays in nonsmoking rooms. In a standard hotel room, ashtrays are scattered over almost every flat surface to make sure careless smokers don't scar the furniture. On the Inter-Continental's nonsmoking floor, the management doesn't put ashtrays in the hallways either, not even by the elevator door. Should guests phone the desk for one, they are reminded that tobacco is not permitted and asked if they might prefer to switch to a smoking room.

Because smoking is a sensitive issue, says Illian, desk staff and phone operators have been given written guidelines on how to handle such problems. Among other steps, the hotel has instructed its staff not to smoke anywhere on the nonsmoking floors and to take care that, if they do use tobacco, that their uniforms don't smell of smoke. Signs are posted in the hallways of the nonsmoking floor to remind guests.

A pamphlet distributed at Quality Inns and local American Lung Association offices urges travelers who want a smoke-free room to speak up and ask for one. Better yet, they should phone ahead and reserve one or ask their travel agent to do so.

SMOKE-FREE EUROPE: Since 1974, the Bethesda-based Non-Smokers Travel Club has been scheduling a yearly program of local and international tours. The idea, as the name suggests, is to put together a group whose members don't smoke.

This summer's international trip is a two-week ramble in August by motor coach through Austria, Germany and Switzerland. In keeping with the club's purpose, the bus driver is also a nonsmoker and meals (where possible) are served in private dining rooms or the nonsmoking sections of restaurants.

The itinerary begins in Vienna and moves on to Salzburg, Munich, Innsbruck, Lake Lucerne, Bern and Zurich. It's a mixture of lovely alpine sightseeing, waltz concerts in Vienna and visits to museums, a Swiss cheese factory and German beer gardens.

Departure is Aug. 13. The land price is $1,295 per person (double occupancy), which includes lodging, a full breakfast and dinner. Round-trip air fare from Washington/Dulles via Frankfurt is $895 per person.

For a brochure, send a stamped, self-addressed (legal-size) envelope to Non-Smokers Travel Club, 8928 Bradmoor Dr., Bethesda, Md. 20817.