A feud between cab drivers and police at National Airport - who have tangled for years in traffic and parking disputes at the crowded terminal - is worsening, according to both sides.

The latest conflict is fueled by charges and countercharges of assault, death threats, disorderly conduct, abusive language and gestures, harrassment and the use of racial slurs, interviews with participants revealed.

"There is a great deal of friction between the drivers and the police," said James T. Murphy, director of Metropolitan Washington airports for the Federal Aviation Administration, which owns and operates the National and Dulles International terminals.

The conflict prompted FAA police officer Robert Conrad, the subject of many drivers' complaints, to ask permission on Monday to carry his service revolver while driving to and from work. Conrad made the request after he was informed by the FBI that cabdrivers . . . were going to waste me."

The drivers, many of them blacks and foreigners, have begun to band together, according to several drivers, and have aired complaints among themselves of "cruel and unjust treatment" at the hands of airport police patrolling the terminal.

Last week the cab drivers held what many described as an emotional meeting at Mount Vernon School in Alexandria at which several drivers denounced the FAA airport police. More than 200 drivers signed a petition calling for Conrad's dismissal, the drivers said.

The drivers are scheduled to meet today with National Airport manager Hugh Riddle to present their case.

As an example of harassment, the drivers point to Patricia Hoyte, a driver with the White Top Co. in Alexandria, who said she was pulled over by Conrad on the night of July 7. Hoyte said the policeman made racial slure against her and Bardia Karminian, a 23-year-old Iranian companion who also drives for White Top. Hoyte said Conrad "took my CB microphone and started beating me over the head with it."

Hoyte and Karminian spent three hours in an airport holding cell and were charged with obstruction of justice by threats or force. Hoyte said she was treated at a hospital for cuts and bruises. "Then Conrad said if I ever came back to the airport, he'd shoot me," she said.

Conrad declined to comment on the case, which is scheduled to be heard in Alexandria's Magistrate Court on Aug. 2.

The chronic taxicab problem at National Airport, Murphy said, "is like trying to stuff five pounds of onions into a two-pound bag."

More than 100,000 cabs a month drive through the constricted area in front of the terminal, he said, entering in a line that snakes along an access road and often blocks incoming traffic. FAA police said they cannot write the tickets fast enough.

"I've made 440 arrests in the last four months," said the 53-year old Conrad. "My highest one day was 70 tickets," he said.

Capt. Robert M. Morehouse, Conrad's immediate superior, said the number of tickets written is up to the individual policeman. "Conrad is just doing his job. And he does it well," Morehouse said.

Other officers interviewed said they often have to break up fights between the cab drivers. "One of them went after another with a tire jack last week," said one policeman.

"We find guns and knives in their cars," said Conrad, pointing to a group of drivers sitting on the grass waiting to pick up fares.

In an interview, Murphy called the traffic circle in front of the terminal "a desirable cab stand."

Murphy also said there is no love lost between Conrad and the cabbies. "It's no secret that the drivers hate Conrad," said Murphy. "Maybe he has been excessively zealous."

Conrad, an ex-sergeant with the Los Angeles Police Department who joined the FAA force in 1972, said the drivers are a volatile lot. "I've personally been assaulted three times in the last month by cabs. I've been called at home and told I don't have long to live."

Conrad reported the threats in a letter three days ago to FAA Police Chief Robert Lawler.

Today FBI agent Don Barthnick reported to me that his office has received information from an informant that cab drivers have followed me home for three nights and were going to waste me," Conrad wrote.

He also contacted Fairfax police, who confirmed yesterday that patrol cars in the vicinity of Conrad's Alexandria home have been alerted and security beefed up.

His request to carry his revolver to and from work was denied, Lawler said, because it was against FAA regulations.

Lawler said that the FAA usually employs 130 policemen for duty at National, but that the force is currently down to 100. Three cruisers and one scooter work each eight-hour shift. The job is equivalent to a GS-5, Lawler said, and pays less than $10,000 a year.

Conrad, meanwhile, said that he has applied for another position - perhaps as a building inspector in San Francisco. "To tell you the truth," he said, "I'm sick of cab drivers."