Alexandria has become to Washington taxis what Panama and Liberia are to ships: a safe haven with little effective regulation. Alexandria has almost 600 licensed taxicabs, more licensed cabs per capita than New York, Chicago or Washington.

"We've become the Panama for a bunch of gypsy tramp steamboat operators!" fumes Alexandria Mayor Charles E. Beatley, who blames the problem on proximity to National Airport and a city taxi board that can't say no. "It's a blight on the city of Alexandria. It's an embarrassment."

In the past decade Alexandria, say Beatley and others, has become the home port for a whole fleet of cabs that are licensed in the city but do virtually all their work out of nearby National Airport. The cabs work the airport despite a city regulation, widely regarded as unenforceable, requiring them to spend 51 percent of their time in Alexandria.

"There are a lot of little old ladies and people on expense accounts who get off at National, and get in our cabs," says council member Donald C. Casey. "They don't know the area, so they get the 'scenic tour' and wind up paying through the nose." Alexandria's lone hack inspector agrees, saying he receives "hundreds" of complaints, some frightening and some funny, about the city cabs.

A two-year moratorium on licensing of new Alexandria cabs recently expired, and the city has received 105 applications for taxi certificates, many of them from foreign students. Some city officials say they fear that the city Traffic and Parking Board will execute its traditional "rubberstamp" approval of these applications, and cause even more problems.

"I think the situation has gotten out of hand," says Vice Mayor James P. Moran. "We've got a proliferation of Alexandria cabs going to the airport for lack of anything else to do, they sit there for hours and then make up the wasted time by overcharging the people they finally do pick up. . . Many of them are very rude, and it gives visitors a bad view of our city."

The mayor and council members are not alone, but there is no consensus at City Hall about a solution. Beatley says he has asked the semiautonomous Traffic and Parking Board, which regulates the industry, to come up with "concrete" suggestions to resolve the taxi dilemma. This fall he expects the council and the board, which is appointed by the council, to meet over the issue.

Some council members say they are loathe to involve themselves in the affairs of city boards, but the traffic board members cannot agree on whether or not there should be a limit on taxis. Board Member C. Peter Schumaier, an economist, believes that the board should let the free market determine the number of cabs. "People wouldn't apply for cabs if they didn't think they could make a living at it," he argues.

Wrong, says Board Member Joseph H. Berardelli, a federal administrator, who also is unsure of the board's legal authority to imposing any moratorium. "We don't need any more cabs. We have the very unwholesome situation of having cabs that operate 100 percent out of the airport," he says. " . . . They're the kind who will soak some kid coming back from a funeral, charge him $15 instead of $4. It's criminal.

"I try to keep everything in perspective. I realize in many cases it's a man's livelihood," says Berardelli, "but I don't like to see the public exposed to the abuses of these people. There's a limit."

Alexandria's hack inspector Marion Huffman has the Sisyphean task of patrolling the city's taxi industry. He alone must check manifests, run record checks on applications, inspect taxis, check out complaints, and numerous other tasks. It is impossible to be everywhere at once, "and the operators know it," he says. Huffman says he gets "hundreds" of complaints about Alexandria cabs and that about 95 percent of them come out of National.

Some taxing tales from the files:

* The driver who picked up an Alexandria woman at National, and insisted several times during the trip that his passenger buy a bag of diamonds for $40. After she refused repeatedly, he spoke to a companion, who pulled a snake out of a bag, and waved it in her face, then tried to charge her double fare. "He threatened that if she complained, he had lots of little snakes and he'd be happy to come over and put them under her apartment door," Huffman remembers. The driver lost his license for a year.

* The New York businessman who was refused service at National when the hacker discovered the would-be passenger was headed only to nearby Crystal City. "I travel a great deal," the man later wrote Huffman, "and I find the cab situation in the Wash. D.C. area to be the worst in the country, and one of the worst in the world."

* The Washington man whose cab ride ended at his NW apartment, with the cabdriver chasing him past apartment security guards and into the elevator to grab the rest of what turned out to be a $2 overcharge.

The situation pleases no one. Not National Airport: "We have more cabs than we need," says airport spokesman David Hess. Not the cabdrivers: "There are too many already," says an Alexandria cab driver from Central America who does much of his driving at National. "We go to the airport because there isn't enough business in the city. We sit in line at the airport two, three hours," he says. "Then you get a $3 fare to Crystal City, what are you going to do?"

Not the cab companies, either, some of which have begun lobbying for tighter controls. "Go down there on Friday when they're lined up all the way to the George Washington Memorial parkway," says Alexandria Diamond Cab General Manager Robert Werth. "There's no way to back out, and they start fighting among themselves. There's no place for them to go to the bathroom so they're urinating on the grass. There are lots of problems," says Werth.

He also argues that the influx of new cabbies has driven professional hackers out of the area.

Alexandria officials who favor a freeze point to Arlington, the home of National Airport. It has 50 percent more population than Alexandria but almost 200 fewer cabs and only six cab companies to Alexandria's 10. Arlington's taxi fleet has been limited to 445 cabs for almost three years, according to the county consumer affairs office. Arlington cabs are not required to spend a percentage of time in the county, nor are they forced to have two-way radios, but Arlington receives far fewer complaints about service at National.

Alexandria's problems began back in 1974 when National Airport ended its exclusive cab franchise and opened the airport up to all comers. It wasn't until 1976 that the Federal Aviation Administration, which owns the airport, drafted regulations requiring the licensing of cabs, and in between hundreds of "gypsy operators," cabbies with no licensing, sprang up to serve the airport. When National clamped down in '76, the "gypsies," as they are called, were forced to find a local base of operations. Many wound up in Alexandria.

Not all cab companies favor a licensing moratorium. Smaller operators believe a freeze would favor large, established companies like Diamond and Yellow Cab and squeeze them out.

Owners of the small All-American and King Cab companies say that a moratorium hurts them by giving them no room to expand. "A freeze is unfair to small companies. We need more cabs to stay in business," says All-American manager James M. Venson. "It seems like some companies get what they want, when they want it."