Two men who served as top financial officials in Prince William County during a period in which the county lost $1.05 million in high-risk securities transactions have agreed to resign, county officials announced yesterday.

County officials would not give a reason for the resignations of Finance Director E. Barrett Atwood Jr. and Fiscal Management Supervisor Ronald Tucker. County Executive James H. Mullen described the decision only as a "mutual conclusion" of the men and other county officials.

Atwood would not comment on his resignation, and Tucker, who co-workers said had not come to work yesterday, could not be reached.

The resignations come as the county is preparing for its lawsuit against the brokerage firm that handled the securities transactions to go to trial.

The $1.05 million in losses were publicly disclosed almost two years ago, about a year after the transactions occurred.

The county filed suit last May against the New York-based brokerage firm County NatWest Inc., and a U.S. District Court judge is expected to rule in October on the county's motion for a judgment in its favor, said County Attorney Sharon Pandak.

A Virginia state auditor found last year that Atwood might be liable for part of the money lost in the so-called "hedge transactions," which Tucker authorized when short-term securities investments totaling $20 million lost money. Atwood has said he did not know the county had authorized such sales. No criminal charges have been filed in the matter.

The auditor also questioned why the Board of County Supervisors was not notified for more than a year after the transactions occurred.

Tucker had worked for the county since 1973, and Atwood joined the government in 1986.