The air traffic controllers' slowdown at Washington National Airport worsened yesterday as both arriving and departing flights were delayed for more than an hour, airline and federal Aviation Administration officials said.

The Professional Air Traffic Controllers Organization (PATCO) issued a statement denying that a slowdown was under way. FAA headquaters avoided the word slowdown and said that the reasons for "lengthening delays" were being studied.

However, Harry Hubbard, the controllers' boss at the National air traffic control tower, said, "it is a slowdown. Today we're probably handling 12 fewer flights per hour that normal and right now there are 26 planes waiting to take off out there." That is an unusually long line for National Airport. It was 4 p.m., normally the start of the airport's busiest period.

The plane that was to carry 107 nirth-grade students back to Omaha after a class trip here was three hours late in landing: the executive vice president of tiny Cumberland Airlines said the controllers were costing him thousands of dollars he could notafford and delays in the Washington area were beginning to distrupt airline schedules throughtout the eastern half of the United States.

Richard Galloway, a sale manager from Chicago who missed a business meeting in Washington yesterday because of a late flight, was irate. "If this is what I think it's over - and I think it's over free trips to Europe - I don't think I have a lot of sympathy for those guys," he told the reporter.

PATCO had warned in a May 23 news conference that job actions were possible if airlines did not permit controllers to make free, unconditional "familiarization flights" to Europe and the Far East.

Controllers say such flights are valuable to give them firsthand knowledge of procedures in the cockpit and they have flown on domestic flights for years. International airlines Pan Am and TWA both said they support the program but cannot guarantee seats on demand.

A slowdown would be an illegal job action because controllers are federal employes John F. Leyden, PATCO president, said late yesterday, "PATCO does not condone nor support such actions, but we understand how the failure of a few airlines to fully institute the familiarization program for controllers can produce frustraction and bitterness on the part of many controllers."

Frustration and bitterness were also emotions expressed by Dale Nicholson, executive vice president of Cumberland Airline. "We really getting the shaft," he said "They're backing us up and vectoring (directing) our planes all over the place. It's unbelievable." Cumberland owns 24 planes and serves Cumberland, Md., Latrobe, Pa., Pittsburgh, Baltimore, Washington, Ocean City, Md., and other area locations.

"We're burning a lot of extra fuel; my passengers are missing connections and its costing us thousans of dollars," he said. "There are too many planes in holding patterns and one of my pilots said he almost had a collition with anothe plane. I can't help them (the controllers). I can only take them to Latrobe."

When queried, Eastern, National, United, TWA and Allegheny airlines all reported delays of up to an hour. Long lines formed at the American and TWA counters at National Airport as passengers tried to make last-minute connections or sought information.

Tom Sawyer, a social studies teacher at Millard Central Junior High school in Omaha, was shepherding his class of 107 ninth graders at gate 14 as they waited for their long-delayed flight home.

"I'm hoping it will be a good learning experience for them," Sawyer said. "Maybe it will teach them about coping with adversity and how to deal with unexpected situations."

But student Michelle Amodeo's response to adversity was to state that "I'm never coming to Washington again."

One man who refused to give his name said he was late for a flight to New York's John F. Kennedy International Airport, where he was going to meet his Polish mother-in-law. She speaks little English and is making her first trip to this country, he said.

"Now I may miss her completely," he said, "and I'm not even sure she likes me as it is."