NEW YORK (AP) _ United Airlines has begun to put the squeeze on frequent-flier freebies.

Alarmed by the mushrooming popularity of the bonus programs and their potential financial impact, the Chicago-based United announced new restrictions Friday that could be imitated by other major U.S. airlines.

The frequent-flier plans reward passengers with free tickets or upgrades to first class after they have flown a set number of miles. United's new program sets up a two-tier system of travel awards.

On the one hand, it increases the mileage that must be accumulated in order to fly free without restrictions. At the same time, the program creates a new category called ''saver miles,'' allowing travelers to qualify for free flights with fewer miles earned than before - but with restrictions on the bonus tickets.

''The frequent-flier programs were getting out of control and, quite frankly, they were heading toward extinction,'' said United spokesman Dan Sheehy. ''We wanted to bring some logic and order to the program.''

Under United's current system, for example, a passenger can get a free round-trip coach ticket to Hawaii after flying 35,000 miles with the carrier. With the new plan, the mileage requirement rises to 60,000 for a normal, unrestricted ticket to Hawaii. With 30,000 miles in credits, a flier can get a restricted free ticket.

A limited number of the restricted tickets will be available for use on each United flight, and they cannot be used during holiday periods.

On the plus side, United is allowing frequent fliers to transfer their travel awards to other people, while currently they can only be given to relatives.

The number of awards available has been reduced from 140 to only 34.

''We're giving a little and we're taking away a little,'' Sheehy said. The airline, a subsidiary of Allegis Corp., has about 4.5 million members in its frequent flier program.

Many observers had expected United to make even more drastic cuts in its program, after one of its senior executives said in a speech in early March that the airline was considering imposing restrictions. John Zeeman, executive vice president for marketing and planning, had said the options under review included requiring that travel awards be redeemed by a certain deadline, and even eliminating free trips and providing only first-class upgrades instead.

Many other airlines have recently slapped restrictions on their bonus programs - most notably by limiting the number of free tickets for any one flight.

Mike Ribero, vice president of marketing programs for Eastern Airlines, said Eastern is studying possible changes to its program, operated jointly with Continental Airlines, like Eastern a subsidiary of giant Texas Air Corp.

American Airlines spokesman Al Becker said the carrier - ranked No. 2 after United - also is studying the issue.

Delta Air Lines, the third largest, doesn't plan to make any changes in its program, said spokesman Jim Lundy.

The U.S. airline industry is facing a staggering revenue loss if the estimated 8 million people enrolled in frequent-flier programs start redeeming their bonuses and bumping paying passengers. The accumulated value of those bonuses is around $1.24 billion, according to Julius Maldutis, senior airline analyst for investment firm Salomon Brothers Inc.

That compares with total industry revenue of around $46.7 billion in 1985, $50.5 billion in 1986 and just over $60 billion last year.