The Air Line Pilots Association and United Airlines, which could strand more passengers in more U.S. cities than any other carrier, are flying to the wire in a tough contract negotiation both sides feel they must win.

A 30-day cooling off period expires at 12:01 a.m. (EDT) Friday and, if there is no resolution, the ALPA says that United's 4,900 pilots will walk out.

The central issue is whether the ALPA will let United hire new pilots for lower wages than it now pays beginners and maintain them for many years at lower pay than current United pilots. "That is the issue," ALPA President Henry A. Duffy said. "If we're able to clear that up, I think the rest of it is there to be had."

The potential disruption from a United strike could not come at a worse time for the traveling public. Domestic airline traffic has set records every month this year after a record year in 1984 as the strong economy continues.

United says that in a strike it would fly some of its schedule with new-hire pilots whom it has been training and with an undetermined number of management pilots. However, industry observers say many ALPA pilots would have to cross the picket line before United could fly a significant portion of its schedule.

United carried 41 million passengers last year, the most of any carrier, about 15 percent of all domestic airline trips or almost one passenger of every seven. United averages 1,577 flights a day to 149 cities in all 50 states and 10 foreign destinations, from Hong Kong to the Bahamas.

Therefore, travel agents who normally would place clients on United flights are trying to find alternatives. Pleasure travelers who have bought advance cut-rate tickets on United will find that other airlines do not have to honor the cheaper rates or guarantee them a seat, which could mean hundreds of extra dollars out of pocket.

"We are seeking protection for our travelers where we can and hoping on hope where we can't," said W.R. Brown, head of AAA Travel Agency, the nation's largest.

Another travel agent, who asked not to be identified, said, "Of course we're booking away from the United or double booking. The clients get angry if you strand them."

Al Becker, a spokesman for American Airlines, United's major competitor, said it has had strong advance sales in recent days and that "obviously, some of that is attributable to the situation at United. But it's impossible to say how much."

The National Mediation Board has scheduled talks in Boston on Monday after more than a three-week hiatus to see if there is any chance of resolving a dispute that has been on the table for more than a year.

"Normally in a one-issue situation, you can work out that one issue," a source close to the negotiations said. "This has been unusually tough, however."

The salary table United wants from the pilots is called a "two-tier" schedule. American Airlines negotiatied such a contract with the Allied Pilots Association in November 1983 and United says it must have the same thing to remain competitive.

American negotiated its contract at a time when pilots were freely available. Those days have changed, however, and several of the lower-paying airlines such as People Exress are having trouble holding crew members who see greener pastures.

Right now, United is healthy financially. It led the industry in revenues last year at $6.2 billion and operating profit of $564 million. Inexorably, however, as American hires more beginners at cheaper wages, its costs will go down compared with United's and place United in a less competitive situation.

"The company's No. 1 objective is to obtain a cost-competitive contract without a strike," said United spokesman Chuck Novak. He said the average United pilot, including captains, first officers and second officers, is paid $91,200 a year for 81 hours of flying per month. A second officer is hired at $22,452. United wants that starting salary to be $21,500. While negotiations have continued, United has placed expansion plans on hold. Boeing, McDonnell Douglas and Airbus Industrie are standing outside United's door with order books in hand, because all know United needs to make a major purchase.

But Richard J. Ferris, chairman of UAL Inc., United's parent holding company, said in a news conference, "We are not in the market at this time for medium-range aircraft until such time as we have secured a cost-competitive agreement from our pilots' union."

Ferris has built a war chest reported to exceed $1 billion. He has more than $400 million in cash on hand. The ALPA's Duffy says that his union is better prepared than ever and that few of his members will cross the picket lines.

United has completed negotiations with two unions, the Association of Flight Attendants and the International Association of Machinists and Aerospace Workers. In both cases two-tier salary schedules were negotiated.

Duffy says the ALPA is willing to accept the same arrangement, but not the better terms he said the company is seeking. Duffy said he has proposed two contracts covering five years, with the two tiers of the salary schedules merging into one at the end of the fifth year. He said that United proposes that the two tiers would merge at the captain's level after many years, 14 at the earliest.

Duffy is also concerned about precedent. Because United is the biggest, he said, "It is the pattern of what this settlement will do that makes it so important . . . . We have a contract open on Delta Airlines amendable at the end of August. And there is no question in my mind that where we end up here will be stamped right on the Delta contract. So it's just a shootout."