A controversial spokesman for a conservative taxpayers group was found guilty yesterday in Alexandria's General District Court of failure to pay personal property taxes for the last three years on his 16-year-old Cadillac Coupe de Ville.

After a 10-minute trial, Judge Robert T. S. Colby ruled that John D. Williams III, president of the Alexandria Taxpayers Alliance, owes the city a total of $645.17 in unpaid taxes, penalties and interest for 1980, 1981 and 1982 in which he admitted paying no city taxes on the car.

Williams, 44, who operates a computer consulting business, said yesterday he will appeal the decision to the Alexandria Circuit Court. He contends that a loopholes in both city and state laws exclude his automobile from the tax.

At his trial yesterday, Williams told Colby that state law requires that a car must be "normally" parked in the city before it may be taxed. He claimed that city law prevents him from parking his car in front of his driveway, and his car is too long to fit in his town house garage on Pitt Street. So, he said he parks in a nearby underground parking garage, "which is not normal," and thus, in Williams' opinion, exempts his car from taxation.

Assistant City Attorney Nancy McBride argued that Williams' arguments are irrelevant. McBride contended that as long as Williams' Cadillac is located in Alexandria, it is subject to property taxes.

After ruling in favor of the city, Colby set an appeal bond for Williams at $25, commenting that he was "sympathetic" to Williams' situation. "He wants to park in front of his house and you won't let him," Colby told the city prosecutor.

"I am delighted," Williams said of Colby's bond decision. "Now I can go to a higher court for $25."

McBride objected to the low bond. But Colby said Williams' car, valued by the city last year at $2,225, could be used to cover the judgment if necessary.

Williams' city tax troubles began in mid-March, shortly after city officials discovered he had not paid city taxes on his car. At the time, Williams was leading a particularly pointed attack on several public housing positions the city supports. He now contends that the city used the tax charges to embarrass him and the taxpayers association, while denying him his right of free speech.

"The entire effort is fraudulent because it is a politically motivated, conspiratorial vendetta," Williams wrote in an answer to the city's charges.

Williams is a frequent speaker at City Council meetings in behalf of his proposals to raze aging riverfront public housing projects and replace them with luxury town houses.

Local officials have denied that the city was out to get Williams.