The International Brotherhood of Teamsters yesterday won its first organizing effort among Washington area hospital workers when employes at Alexandria Hospital chose it to represent them following a bitter campaign.

The Teamsters will be the first union to represent workers at any Northern Virginia hospital. Nationally, the 2.5 million member union has mounted successful organizing drives at hospitals in New York City and Michigan.

The union said that if it was successful in organizing workers at Alexandria Hospital, it would launch organizing campaigns at other hospitals in the Washington area.

The Teamsters union was elected bargaining agent for 450 service and maintenance workers at Alexandria Hospital. The vote was 210 for representation by the Teamsters, and 149 against, with two challenged ballots and three that contained no votes.

Hospital officials said they will decide in a few days whether to file a legal challenge to the election results with the National Labor Relations Board.

Mark Goldberg, an attorney for the 414-bed nonprofit hospital, said an objection to the union's conduct in the campaign that preceded yesterday's election may be filed next week.

He said a series of letters mailed to hospital employes "may have misrepresented the hospital's position on issues" such as job security and salary.

Alexandria Hospital administrator John Edward Sweet Jr. issued a statement after the vote saying, "a union is not [in the] best interest" of employes or patients.

Job security was a major factor in the vote. Alexandria Hospital was the only major Northern Virginia hospital to lay off employes this year, according to hospital spokemen in the area. Last July, it unexpectedly fired 30 people to counterbalance an anticipated $4 billion deficit.

Union activity started after the workers were fired.

The hospital claimed that the union would take more money from employe paychecks in the form of dues and other charges than it would gain for them in salary increases. The union denied that allegation.

Ben Hylton, secretary-treasurer of Teamsters Local 246, which won the election at Alexandria Hospital, said yesterday he has already begun seeking to represent the 1,200 workers at the 350-bed Arlington Hospital.

But Robin Rogoff Star, a spokesman for Arlington Hospital, said, "so far, we are not aware of any union activity."

The American Federation of State, County and Municipal Employes represents about 5,000 hospital workers in the service and paraprofessional fields at hospitals in the District of Columbia and Maryland. Other unions representing area hospital workers include the District of Columbia Nurses Association and the National Union of Hospital and Health Care Employes, District 1199.