Mail carrier Darlyn Hunter made her usual letter deliveries on Rhode Island Avenue N.W. the other day, and like many of her postal co-workers, said she did not want to think about the possibility of a postal walkout this week.

"I really haven't gotten into it," she said. "When I came in three months ago they were talking about a strike but we're not supposed to strike. It's illegal."

A cross-section of local postal workers and their leaders indicated in interviews last week that they do not want to strike any more than the public wants a strike. But the workers also say that they might be forced to the illegal action to get their demands in contract talks now in progress between the four postal unions and the United States Postal Service.

The contract between the nation's 550,000 postal workers and the postal corporation ends at midnight Thursday.

The Federal Mediation and Conciliation Service, which is meeting with both sides, reported that progress had been made in the bargaining, but cautioned that the most difficult issues are yet to be resolved.

The parties met both Saturday and Sunday and talks were reported continuing last night.

If there is a strike, several area governments and private companies have drawn up contigency plans to deliver some of their mail.

Officials of the Washington Gas Light Company and the Potomac Electric Power Company plan to use office workers to hand-deliver bills to their customers' homes.

Tax officials may have special problems to confront.

"We have not thought about it and we don't want to think about it because we're hopeful it will be resolved," said Douglas L. Jernigan, Montgomery County's tax collector, who has 170,000 property tax bills to mail this week.

"We'll be in a world of trouble" with a strike, he said, "and we will have to tell people to come in and pick up their bills."

Prince George's officials expect to mail out their 180,000 new tax bills early this week. Some county employesare to make sure all the bills are in the mail before Thursday, a county tax officials said.

Grady Williams, head of the payments bureau of the District's Department of Human Resources, said that if there is a strike, he will have to ask the city's 101,000 welfare recipients to come to various DHR officies around the city to collect their checks.

Officials at the American Security Bank, Maryland National and United Virginia Banks are still trying to decide what their respective companies will do to get out payments and statements to customers.

"It's very very difficult to plan in advance because we don't know where a strike will be or for how long," said Melvin Chrispman, senior vice president and cashier at the Riggs National Bank. "It will be just a big mess, frankly. If it's of short duration, most of our mail we'll simply have to hold."

The National Education Associateion mails out 40,000 letters, books, pamphlets and reports daily, and "it's going to pile up," said Robert Gruenberg of NEA public relations. He expressed the view of many officials in the national organizations that are headquartered here.

Post Office officials are not talking about what they plan to do if faced with a work stoppage, said Lou Eberhardt of the Postal Service public relations office.

Eberhardt would only confirm the broad outlines of a "strike contingency plan" which the Washington Post revealed in the spring. The plan includes using federal troops to guard and move the mail, embargoing most types of mail and requesting customer pickup of letters and packages.

The Defense Department said over the weekend that it has a contingency plan that has been in effect since 1970. If there is a "work stoppage," the department said, the Army would provide troops to help deliver the mail. The plan, called "Graphic Hand," will be used only if the Postmaster General "requests assistance and the President declares a national emergency," the department said.

"It's a frightening prospect," said Leo Dougherty, president of the Silver Spring local of the National Letter Carriers Union, who knows he can be arrested and jailed if a strike occurs."When you come to work for the post office you sign a statement saying you will not strike," he said.

"I hope they can come to an agreement," said mailman Paul S. Barnes, during his rounds in the 100 block of U Street NW.

"I have a family to support. I'd hate to go out and try to get odd jobs to make ends meet. But if they (the union leaders) say strike I have no alternative. I'm part of a union. Let's just hope it doesn't happen," said Barnes, an 11-year veteran of the Postal Service.

"A strike has to be considered in the light of public opinion," said Dougherty of the letter carriers' union. "We don't have the support of the public. Postage rates have gone up. The American public thinks they have skyrocketed."