Two incidents of fighting occurred at Alexandria's T.C. Williams High School this week, resulting in the suspension of several students, officials said yesterday.

The first incident, on Monday, involved as many as a dozen teen-agers who brawled on a paved road separating school property from the city-owned Chinquapin Park, officials said. No one was seriously hurt in the lunch-period flare-up and no arrests were made, according to police and T.C. Williams principal Tony Hanley.

In the second incident, on Tuesday, one student hit another, Hanley said.

In each case, black and white students were involved, and one school board member, who requested anonymity, described the first incident as "a racial flare-up." This board member said that in the Monday incident, "what started as a stupid fight went immediately into something with racial overtones. Nobody got seriously hurt, but things have been tense all week."

School board member John O. Peterson, who is black, denied that there was a racial motivation. "It was just a fight," he said. "The main concern we have at T.C. Williams is overcrowding."

Hanley said, "any school has violence, this is the type of thing you expect in the spring when the weather is warm and it's too early to study for finals . . . Everything is calm now."

Hanley said that on Tuesday he had additional school administrators patrol the grounds to "keep peace" between black and white students. He said those administrators stayed on the grounds Wednesday and yesterday.

Several students were suspended as a result of the Monday incident, Hanley said. Both of the students involved in the Tuesday fistfight, which he said apparently was unrelated to the Monday melee, also were suspended.

Alexandria Police Sgt. Ron Uhrig said he is investigating the possibility that the first incident stemmed from a dispute over drugs.