The men – aged, 27, 28 and 30 – were arrested in Strabane and Derry City by detectives investigating the criminal activities of the INLA.
The PSNI they have now been released unconditionally.
The arrests were in connection with an incident in 2019 during which a number of individuals holding firearms posed for a photograph in front of INLA graffiti in the Galliagh area.
Detective Inspector Boyd said: “This search and arrest operation is part of an ongoing investigation into the criminality of the INLA in the North West.
“Dismantling this group is a priority for police due to the threat, risk and harm they pose to our communities. The breadth and depth of their criminality has a major impact on our communities in Londonderry and Strabane.
“The INLA claim to be protecting their communities by shooting people they accuse of being involved in crime.
“In reality, it is they who use violence and intimidation to control and exploit their communities.
“I condemn the INLA’S use of social media to spread the fear of violence they seek to instill in their communities.”