ALEXANDRIA, Va. (AP) _ A veteran Army intelligence officer, charged with filing false statements to cover $158,000 advanced to him while he operated a covert Army operation, went on trial Monday in U.S. District Court.

The trial of Lt. Col. Dale E. Duncan is the first to stem from a secret, two-year Army investigation of alleged financial improprieties by some of the service's intelligence and special operation units.

In opening statements, Assistant U.S. Attorney Theodore Greenberg said the government would try to prove that Duncan, who ran Business Security Internation in Annandale, Va., defrauded the government by turning in false vouchers and receipts.

Business Security International, which purported to be a civilian security consulting firm, was actually a military-run organization ''to prevent hostile foreign elements from discovering what a group of small Army units were doing,'' Greenberg said.

The company was formed in July 1983, but disbanded in December of that year after allegations were made against Duncan by a former subordinate, Warrant Officer Thomas P. Golden.

The allegations led to an investigation by the Army's inspector general, Army financial officers and the Justice Department.

Duncan's seven-count indictment includes charges that he claimed $796 for a free plane ticket; that he claimed he paid $8,400 to lease a plane in Florida when someone else had provided the money, and that he filed an invoice for $56,230 for communications equipment that he had never purchased.

John M. Dowd, Duncan's attorney, disputed the charges and said that his client had asked for an audit of Business Security International.

Duncan also faces Army court-martial proceedings.

Master Sgt. Ramon Barron, a former Business Security International employee, was acquitted of defrauding the government last December in a court- martial.