IN THE PAST, airline passengers came in only two classes: the rich or fortunate, who enjoyed the aloof luxury of a first-class seat, and the rest of us, grouped together in the often-crowded confines of an economy-class cabin.

Now a third class is being offered--business class, aimed at the business traveler. It seems to be enjoying popularity, primarily on overseas flights but also on a number of domestic routes. In terms of comfort, business class is not as "elaborate" as first class, as one airline sales agent describes it, but it's "10 steps above economy class."

On some airlines, 60 percent or more of the passengers are business travelers, and for the airline industry as a whole, the figures are 52 percent business, 48 percent vacation. The airlines see the new business class as a way of catering to these profitable customers. Frequent-flyer bonus programs offered by most U.S. airlines similarly recognize the value of the business traveler.

Travel Weekly magazine calls development of business class "one of the major changes of recent years" in the air transportation industry.

The idea is to provide more space, more attentive treatment and a quieter atmosphere than can usually be found in economy class at a price substantially less than is charged for first class. This is so business travelers can either relax more easily, presumably arriving at their destination rested and more fit to negotiate a contract, or they can catch up on office work without the interruptions of chatty fellow passengers.

The added amenities can include any or all of the services normally found only in first class: wider seats with more leg room, fewer seats in a row, reclining slumber seats, free cocktails (economy-class passengers pay $2.50 a drink), free headsets for in-flight movies, jazzier meals, real silverware and china instead of plastic, use of the private airport lounge and special baggage handling (first off the plane).

As anyone who has sat three abreast in economy class knows, passengers can't always count on getting any work accomplished, no matter how good their intentions. Two businessmen on a recent flight from San Francisco to St. Louis learned this to their chagrin. After takeoff, they immediately opened their brief cases, earnestly shuffling papers and jotting notes. But the third passenger in their row, sitting in the window seat, soon thwarted that.

She was a child, no more than 7 or 8, traveling alone. Friendly and pleasant, but restless, she peppered the two businessmen with questions about the plane, the meal, the time, the location of the restroom, all of which they answered agreeably. In no time at all, they had closed up their briefcases and were devoting their attention alternately to her and, when they could find a moment, to the airline magazine.

That kind of situation could make the pair prime candidates for business class, suggests Dave Venz, a spokesman for Trans World Airlines, which has adopted the three-class system in a big way. "We see a definite need for it. The business traveler is truly the industry's bread and butter.

"One of the things that a frequent traveler finds attractive," he says, "is that it does put him or her in a separate cabin, where they can get their work done." TWA added business class (they call it "Ambassador Class") to its international flights in 1980 and expanded it to transcontinental flights in January of 1982 and to all its wide-bodied flights last fall.

At the moment, most regularly scheduled airlines offer some form of business class on transatlantic or transpacific flights. British Airways reserves the upper lounge of its 747s for non-smoking business-class passengers, with smokers being seated on the lower level behind first class. Singapore Airlines similarly sets aside the upper lounge for business men and women, advertising it as "a spacious luxurious retreat where they can enjoy a well-deserved rest from the hectic business world."

Business class "is a lifesaver," says one American executive based in Singapore. "Especially when your company won't pay for first class."

Washington travel agents who handle a large number of commercial customers say many of their clients request business class for long-haul trips. "We use it quite a bit," says Mary Kay Matthews of Van Slycke and Reeside Travel Associates. Andy Spielman of Waters Travel Service is finding the same interest among his clients. First-class rates may be "too stiff" for companies to justify, he says, but some will permit an employe to upgrade from economy to business class. Some otherwise tightfisted firms have policies permitting upgrading if a flight exceeds eight or 10 hours.

Spielman himself recently returned from London in business class. "It was very, very comfortable. The major difference was that you didn't have that hemmed in feeling."

On flights within the United States, however, the availability of business class is much more limited. In addition to TWA's domestic service, Republic Airlines, which flies to more than 150 cities coast-to-coast, has established with it calls a "Business Coach" class on almost all of its flights (though it doesn't have a first class). Pan Am offers its "Clipper Class" for the business traveler on transcontinental and selected New York-to-Miami flights. And last January, American Airlines inaugurated a business class on its transcontinental flights.

So far, these carriers seem to be enthusiastic about the new program. "We're having good luck with it," says Walter Hellman of Republic. "It's an enormously successful undertaking," agrees TWA's Venz.

Nevertheless, other airlines are either waiting to see what happens in the industry or have considered and rejected the idea of a domestic business class, at least so far. "We don't feel it's necessary," says spokesman Chuck Novak of United Airlines, one of the nation's largest carriers, which does have a business class on its new routes to Asia. That sentiment is echoed by Eastern Airlines, which notes that many of the places it flies to are vacation, not business, destinations.

One word characterizes business-class air travel: "inbetween." On most flights, the seats are physically located between first class in the front and economy in the rear; the amenities are better than economy but not as good as first class; and the ticket prices are inbetween.

On domestic flights, the difference in price between a full-fare economy ticket and a business-class ticket generally is not substantial. Business travelers frequently must pay full economy fare anyway because their last-minute schedules disqualify them for a discounted rate, which may require advance ticket purchase, among other restrictions. For a long time, frequent business flyers have grumbled that they pay full economy fare while once-a-year vacationers--who may occupy the seat next to them--get the same trip at half price on a super-saver fare.

For a one-way ticket from Dulles to San Francisco, TWA currently charges $539 for a first-class ticket; $356 for Ambassador (business) class; and from $229 to $410 for economy. Pan Am Clipper Class from Washington to Los Angeles (via New York City) is $489, compared to $566 for first class and $423 for full-fare economy. Republic, which has the largest selection of domestic business-class flights, charges $10 more for its Business Coach than for a nondiscounted coach fare.

The price spread tends to increase on the longer hauls. On its New York City-to-London route, a round trip on TWA, for example, costs $3,858 for first-class; $1,912 for business class; and $880 for a full economy fare. In this case, although Ambassador class is substantially more than economy, "a lot of companies," says spokesman Venz, will "spring" for it on the grounds that "if we think enough of the guy to send him to London and the deal's that important," then the added expense is worth it.

Has the development of business class improved airline travel? Dan Smith, consumer affairs spokesman for the International Airline Passengers Association, thinks the frequent flyer is getting "legitimate benefits." One disadvantage, however, is that business class has added yet one more confusing factor to the already complicated fare structure.

There is no established standard for business class, and each airline offers its own menu of services. As a result, Smith recommends that passengers making reservations determine specifically what amenities will be provided for the extra cost.