PC Maurice Allen (47) and Pc Damien Cobain (42), both of Durham police, pleaded guilty at Newcastle Crown Court to misconduct in a public place.
Allen also faced 16 charges of theft relating to various firearms but did not enter a plea.
Both men were granted unconditional bail to appear at the same court on February 26.
The pair were arrested after a burglary at a farmhouse in north Durham, in which one of the items stolen was a rifle, which the owner said he had bought from the police.
A seven-month investigation by the Independent Police Complaints Commission examined claims that weapons handed in by the public for safe disposal were later sold.
A police spokesman said that all the firearms had been accounted for and there was nothing to suggest that any of them had been used in criminal activity.