Nine years ago Woon-Sun Wu, an arrival from Hong Kong, was charged by the Washington office of the Immigration and Naturalization Service with being an undocumented worker--an illegal alien. At a hearing, Wu admitted that he was here illegally and agreed to leave the country. He is still here.

This case is typical of thousands, according to INS officials, in a system gone so awry that officials believe only a tiny fraction of the illegal immigrants arrested in the Washington area ever leave the country.

Last year, for example, the INS Washington field office, which covers the District of Columbia and Virginia, arrested about 1,000 persons believed to be illegal immigrants. Although most of those conceded their illegal status and volunteered to leave the country, they never left, INS officials said. Only 10 were known to have been deported, according to Narciso Leggs, a senior INS deportation officer.

Others, along with an uncounted number over the years, have simply remained here because INS does not have the manpower to follow their cases or because they have clogged the courts with appeals that take years to be heard, INS officials said.

"They can beat the system by using the system," said Kellogg H. Whittick, who recently retired as Washington INS district chief. He described his office as a "revolving door" for illegal aliens who can delay their departure indefinitely by appealing, or simply ignoring, the rules.

In Wu's case, according to court documents, after conceding his illegal status, he volunteered to leave the country in 1974. Subsequently, he appealed his status five times and failed to attend scheduled deportation hearings at least three times, according to court records. The case is still in the courts.

Mark Mancini, Wu's attorney for the last six months, said his client has been allowed to stay here for years because "INS simply never followed up," and because "he is only taking advantage of the various forms of relief available to him under the law."

Reached at the Chinese restaurant in Richmond where he now works as a cook, Wu, now 38, referred a reporter to his English-speaking brother-in-law, who referred the inquiry to Mancini.

"If the INS does not insist and enforce the departure on the day the alien concedes his deportability, they might as well forget it," Mancini said. Even if the alien has agreed to leave, if he then appeals, he can usually stay indefinitely, Mancini said. "It is almost incomprehensible to most people that this can be true, but it is the way the system works," he said.

INS attorney Don Couvillon said the Wu case "is a splendid example of how if you really do not want to leave this country, you don't have to . . . . we do the best job we can under adverse circumstances."

Some of the problems that INS Washington field office authorities say they encounter include:

* A backlog of more than 8,000 cases in the deportation section of the office. The three-member staff assigned to monitor them works without a computer.

* Only one immigration court attorney responsible for prosecuting the more than 1,000 immigration cases waiting to go to trial.

* The aliens' increasing awareness of the cumbersome nature of the system and the means of exploiting its weaknesses. About 20 percent of the alleged illegal immigrants apprehended never attend their preliminary hearings, and most of those are never caught again, officials said. After their arrest, many agree to voluntary departure, but then decide to appeal and remain here as that process goes on, said officials.

* INS policy that has reduced bond. The average bond today costs $500 to $1,000, as opposed to $2,000 or more in previous years. Whittick, the former head of the Washington field office, said overcrowded jails had no space for those who could not afford to post the higher bond.

* Understaffing in most sections of the local INS office. Ten agents are responsible for investigating cases in D.C. and Virginia.

Duke Austin, a spokesman for the INS national office, said there are no statistics to determine the extent of such problems at other INS district offices. "I think it's going to vary from place to place," he said. "Certainly there are backups" in cases waiting to be heard.

Richard R. Spurlock, director of the INS office in Baltimore, which covers Maryland, said his office, with a backlog of 900 cases, is not facing problems on the scale of the Washington office. He said he believes there are fewer illegal immigrants in Baltimore than Washington, New York or other cities.

Whittick said the Washington area attracts large numbers of illegal immigrants because of the number of service jobs here, and because there is an established base of friends and relatives here.

Washington field office INS agents, increasingly aware of the futility of their efforts, characterize their work as a "joke," "pointless" and "frustrating."

Whittick said that INS agents will continue to be ineffective until Congress revamps immigration laws that allow the illegal immigrants to stay here.

"One section of the law says one thing and another section says something else. It's like a cop giving a person a traffic ticket for running a red light and then turning around and saying, 'Well, if you back up you won't get the ticket,' " said deportation officer Leggs. "It's just a merry-go-round."

One example officials like to give is the "suspension of deportation" law, which says a person who has been in this country for seven years cannot be deported. "The one who avoids being caught the longest gets the benefit," said Mark Riordan, a local INS investigator.

In spite of their complaints, district INS agents in the past nine months have been charging more people with being illegal aliens than ever before, officials said. Because of an appeals court decision early last spring giving the INS here broader authority to obtain warrants, and the simultaneous end of what Whittick described as particular problems involving Iranians, Cubans and Haitians, the local office has been able to focus more on catching illegal aliens.

"Until we were able to take care of the Cuban boat-lift mess, the Haitian refugees and the Iranian students who had overstayed their visas that President Carter wanted us to arrest and send back, our hands were pretty much tied," said Whittick.

But the increased raids and arrests are only adding to the backlog without lowering the aliens' population in Washington, officials said. INS investigators say they feel as though they are on a sinking ship.

Steve Stephanadis, assistant INS district director for investigations, said, "For the past two years the work force that I could put on the street I could count on two hands."

"Now just what is it that you expect of this office in the nation's capital? How do you want us to respond to the many problems that we have?" Stephanadis asked rhetorically. "You and I know there is one hell of an alien population in our area."

When asked for his estimate, Stephanadis said that going to a "gypsy soothsayer" would be as accurate as any statistics that might be available.

One plan developed by officials to deal with the manpower problem has been to show force in a way that makes the local INS office look more powerful than it really is.

"We try to give the appearances wherever we can to make them believe we have sufficient force so that they will stay away. If the aliens think we don't have the manpower to do the work, they will actually be attracted to this area. It would be considered a free port for them," said Whittick.

Added Stephanadis, "I'm still way in the hole in manpower . I can't come upstairs to the district director's office and say, 'yes, I can see daylight now.' We're still just treading water. That's all we're doing right now."