Police executed warrants at Fyshwick and Bonner on Monday when they allegedly found a phone and computer with video and image files of child abuse material.

The search came following an investigation by the ACT Policing Joint Anti Child Exploitation Team with the Australian Centre to Counter Child Exploitation.

Police say they also seized two "incorrectly stored" registered firearms and ammunition.

The 38-year-old Bonner man was charged with possessing or controlling child abuse material obtained or accessed using a carriage service, possess child exploitation material, and fail to store firearms correctly.

His ACT Firearms Licence was suspended.

The man was arrested and given bail at the ACT Watch House until April 6. Police said they expected further charges would be laid.

Members of the public who have any information about people involved in the possession or sharing of child exploitation material are urged to call Crime Stoppers on 1800 333 000.

You can also make a report online by alerting the Australian Centre to Counter Child Exploitation via the Report Abuse button at www.accce.gov.au/report.