James Edward Jackson, 36, claims that he was mistakenly arrested by Alexandria police last April on a charge of assaulting a woman. Then, he says, he was arrested a second time in the case, then a third and a fourth, until he had spent five nights in the Alexandria jail accused of something he had not done.

The problem according to a suit Jackson filed yesterday in U.S. District Court in Alexandria, is that his name is the same as another man (who is five years younger) who is accused of beating up the woman.

Within less than two months, starting last April, the elder Jackson was arrested or detained by police four times to appear in court to answer the charge, according to court records and the suit.

In the suit, the elder jackson asks $20,000 each from the city, Police Chief Charles T. Stroble, Officer Ronald P. Snuffer and any other officers who may be involved. The suit alleges infringement of 14th Amendment rights by illegal arrests and searches.

Deputy Alexandria Police Chief Clyde Scott said yesterday that a warrant had been issued for one person, and another was arrested, but he added that he couldn't comment "yet as to exactly what happened because of the litigation."

The Jackson who filed suit lives with his sister in Alexandria, according to his attorney, James E. Mullins. The residence of the other Jackson is unknown.

According to the suit and court records, a judge dismissed the assault charge following the last court appearance of the "wrong" Jacksons.