A veteran Army intelligence officer went on trial yesterday in U.S. District Court in Alexandria on charges that he filed false statements to help account for $158,000 advanced to him while he ran a covert Army operation.

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

In his opening statement to jurors, Assistant U.S. Attorney Theodore Greenberg said the government would seek to prove that Duncan, who ran Business Security International in Annandale, 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, set up in July 1983, was disbanded in December 1983 after allegations were made against Duncan by a former subordinate, Warrant Officer Thomas P. Golden. Those allegations set off major investigations, some of them still continuing, by the Army's inspector general, Army financial officers and the Justice Department.

Duncan's seven-count indictment charges that he claimed $796 for a plane ticket he actually had received for free; that he claimed he had 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, although he had never purchased it.

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

"At no time did Duncan submit or tender an . . . invoice as a receipt" and when the audit was completed, there was "not a nickel missing," Dowd said.

In addition to the federal charges, Duncan and two other soldiers who worked with him in the Army's Special Operations Division, headquartered in the Pentagon, are facing Army court-martial proceedings. One hearing, that of Lt. Col. James Longhofer, begins next week.

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