NORFOLK, Va. (AP) _ A woman who sued one city alleging she had suffered job discrimination because she was black has filed a lawsuit against Norfolk alleging she was denied a promotion because she was white.

In response to the action filed in U.S. District Court, the city said Theresa Mulqueen Skeeter ''cannot allege on one occasion membership in the black race, and then, when personal gain can be had under the circumstances, on another occasion allege membership in the white race.''

She is seeking $2.2 million in damages from the city and several city officials.

In a 1983 suit against Suffolk, which she lost, Ms. Skeeter said she was raised as a black, attended all-black schools in Suffolk in pre-integration days and socialized with blacks.

The judge in that trial said he was puzzled.

''Well, I see your mother and I see your father and I see your sister, and they are sitting right here in the courtroom ...,'' said U.S. District Judge Robert G. Doumar. ''And I look, and I can't find where you would have any basis for calling yourself black. That's what's giving me some problem.''

In the current suit, Ms. Skeeter alleges she was hired as a senior clerk- typist with the promise that within four months she would be promoted to ''principal bureau secretary.'' She alleges she was denied the promotion because she was white and blacks were promoted ahead of her.

Ms. Skeeter's lawyer, Edward A. Fiorella Jr., said he was unaware of her claim to be black in the earlier suit.

''She told me there were blacks in her family. ... She looks white to me, and if she is deemed black, it's a surprise to me,'' Fiorella said.

Named in the suit with Norfolk were her former supervisors, all of whom are black. They swore in affidavits that they believed she was black.

The director of the city's Department of Human Resources, Clarence A. Cuffee, said last week in an affidavit that he believed Skeeter was black because of her physical features, as did Catherine D. Kearney, who had been Skeeter's supervisor at the Huntersville Multi-Purpose Center.

''Logically, defendants could not have intended to discriminate against a plaintiff on her now alleged race if they thought she was black,'' the city said in court papers.

Whether someone is black, for legal purposes, is a matter of self- identificat ion and the community's perception, Assistant City Attorney Andre A. Foreman wrote in a brief filed last week.

''The term 'race' under the various statutes relied on by plaintiff in this action is not subject to a precise definition,'' Foreman said.

Ms. Skeeter ''considers herself a black American and has actively pursued legal remedies for alleged discrimination on the basis of her race (black),'' the city's brief said. The city included a copy of Skeeter's birth certificate in court papers. It says she and her parents are ''colored.''

The city acknowledged that determining a person's race may not always be easy, ''given that our country is a melting pot for many races,'' Foreman wrote.