A group of prominent Arlington Republicans, including White House press secretary James S. Brady and former national security adviser Richard V. Allen, asked the Justice Department for help yesterday in replacing the county's at-large electoral system with one based on geographical districts.

In an eight-page letter to Attorney General Edwin Meese III, the group charged that Arlington's system has the effect of diluting the voting strength of the county's blacks. It notes that "no black person has ever been elected to any local office since the days of Reconstruction after the Civil War."

About 9 percent of Arlington's 155,000 residents are black.

County Democratic officials challenged the appeal, saying that the current at-large system is not discriminatory.

"Every time the Republicans see their political prospects at a dead stop, they raise this issue," said County Board Member John G. Milliken, a Democrat. "This is purely a political gambit."

Milliken, who is running for the Democratic nomination to oppose Rep. Frank R. Wolf, added that the issue is "a legitimate one which has been debated periodically for as long as I have been active in county politics."

In the past three years, the American Civil Liberties Union has sued several cities in an effort to eliminate at-large voting that it said effectively discriminated against blacks.

Last month, the town of Warrenton, Va., agreed to an ACLU proposal to switch from an at-large electoral system to a ward system.

"The Department of Justice has been moving with some vigor breaking up these things," said Sherman Pratt, referring to at-large elections. The goal, he said, is to "get a district where most of the blacks live." Pratt ran unsuccessfully for the County Board in 1973 and was a plaintiff in an unsuccessful suit to eliminate Arlington's at-large system.

The letter -- signed by 14 persons, including former GOP board members Walter L. Frankland and Dorothy T. Grotos -- states that no board member has been elected from the southern half of the county, where most blacks live, for 25 years. But Milliken disputed that, saying that he lives in the southern part of the county.

Democratic officials in the county say the problem is more complex than Pratt suggests because Arlington blacks are concentrated in three parts of the county: Nauck, Central Arlington/Arlington View and Highview Park. And as those of Hispanic and Asian descent move to Arlington, the number of blacks as a percentage of the voting population is decreasing.

The county is governed by five board members, each elected for four-year terms on a staggered arrangement. Before 1930, Arlington had an electoral system that consisted of three districts in which candidates for the board were required to reside.