When you call your favorite travel agent to book an airline flight, it is possible you will get neither the most convenient nor the cheapest, because of the way a computer tells the agent what flights are available.

If that's upsetting, consider the effect on the airline executive who has either the most convenient or the cheapest flight, but who does not get the booking.

Most of the computer reservation business belongs to industry giants American and United airlines, which acknowledge that biases in the systems give preferential listings to their flights.

A number of smaller airlines, led by Continental, allege that American and United have used their computer systems over the past few years to:

* Influence travel agents to book passengers on American and United when smaller competitors had equal or better service.

* Collect important competitive information about other airlines that helps American and United determine market strategies.

* Develop such dominance in the computer reservations business that no one else could enter and hope to compete.

The Civil Aeronautics Board considered the problem for months, prepared a long report that established that there is bias, but punted to Congress.

The Justice Department started a civil investigation more than a year ago to see if there are antitrust implications in the way computer reservation systems can be used by owner airliners, and has yet to say a word other than that the investigation is continuing.

Last week the House public works and transportation aviation subcommittee held three days of hearings on the matter, where there was widespread disagreement whether the government should intervene--require American and United to eliminate the bias or sell their systems--or leave the problem to market forces and industry cooperation.

The big issue is something called "display bias." The American Airlines Sabre computer reservation system slightly favors American flights in the display that appears on a travel agent's screen when information is requested about how to get from Point A to Point B at a given hour and date; the United Airlines Apollo system slightly favors United's flights in its displays.

Apollo or Sabre systems have been sold or leased to 75 percent of the computerized travel agents, which means most of the major agents. Thus, the two largest airlines in terms of both revenue passenger miles and revenues in 1982 control the reservation and ticketing networks on which the other airlines are dependent. Travel agents sell about two-thirds of all airline tickets.

Clark H. Onstad, vice president of governmental affairs for Continental Airlines, called for federal relief.

"If the business strategy of intentionally biasing consumer information to deceive the public for commercial profit is allowed to fluorish in air transportation, how long will it be before this practice spreads to banking, housing, insurance, hospital care and other sectors of the economy?"

Robert L. Crandall, president of American Airlines, counterattacked: "Having successfully developed and marketed our system, we now find ourselves subject to criticism by carriers that did not choose to make similar investments." If efforts to regulate computer reservations systems succeed, he added, "the trunk carriers will be stripped of one of the few unique competitive advantages they possess--and airline competition itself will be the loser."

In response to a question, Crandall said, "We obviously use all the information we can get our hands on to induce people to fly American."

Committee members themselves wrestled to find middle ground. Rep. Norman Y. Mineta (D-Calif.), subcommittee chairman, said in an interview that "this is not the kind of thing that can be easily solved with legislation," and said he would probably ask the CAB to institute a consumer protection investigation that could result in rule-making.

Rep. Elliott H. Levitas (D-Ga.) said at one point during testimony that if American and United have developed "a better mousetrap, that's what it's about." Then he said, "If it's skewed, that's another thing."

Other airlines can buy so-called "co-host status" in Sabre and Apollo, and get their schedules displayed on something approaching equal status with American's and United's.

Michael Muse is president of Muse Air Corp., one of those little airlines deregulation has spawned. Muse provides service in the Southwest, concentrating on the Dallas-Houston market. "Our primary problem with the Apollo and Sabre systems," he testified, "is the exorbitant rates they are charging, the rapid rate at which the charges are increasing and the virtual certainty of more escalation in the future.

"The rates are so high that the two carriers which own these systems are in effect confiscating the cost efficiencies and savings of deregulation . . . . "

And Alfred Kahn, the economist and former CAB chairman, came out four-square in favor of regulating airline computer systems because, unlike airlines, they look to him like a natural monopoly, a utility of sorts. "It seems to me conceivable that the only way of operating these systems consistently with fair competition is to divest them from their present owners and put them in neutral hands," said Kahn.

This brought a remark by Levitas that Kahn, a champion of airline deregulation, is not afflicated with that "hobgoblin of little minds, consistency."

Travel agents agreed that it is possible to get around the biases with a number of commands to the computer. However, studies have shown that 90 percent of the tickets sold are sold off the "first screen," the first display the travel agent reads. A competitive airline's better flight will probably--but not absolutely--appear on the first screen, but may not appear on the first line.

The two biggest travel agent associations disagree on what should be done. Larry S. Clark Jr., director of the American Society of Travel Agents, said "the industry should have an opportunity to resolve" the issues itself through a standards committee that would develop criteria and principles "that could attract voluntary adherence from all affected parties."

But the Association of Retail Travel Agents said the computer system owners "should be required to utilize them in a fair and unbiased manner." Jay B. Rea, chairman of that group and owner of a travel agency that uses Sabre, testified that "the tendency is strong toward becoming more responsive to the airline that supplies you the system, making that airline more equal than the others."