The study of cluster post starburst galaxies gives useful insights on the physical processes quenching the star formation in the most massive environments . Exploiting the MUSE data of the GAs Stripping Phenomena in galaxies ( GASP ) project , we characterise the quenching history of 8 local cluster galaxies that were selected for not showing emission lines in their fiber spectra . We inspect the integrated colors , and the H \beta rest frame equivalent widths ( EW ) , star formation histories ( SFHs ) and luminosity-weighted age ( LWA ) maps finding no signs of current star formation throughout the disks of these early-spiral/S0 galaxies . All of them have been passive for at least 20 Myr , but their SF declined on different timescales . In most of them the outskirts reached undetectable SFRs before the inner regions ( “ outside-in quenching ” ) . Our sample includes three post-starforming galaxies , two passive galaxies and three galaxies with intermediate properties . The first population shows blue colors , deep H \beta in absorption ( EW > > 2.8 Å ) , young ages ( 8.8 < \log ( LWA [ yr ] ) < 9.2 ) . Two of these galaxies show signs of a central SF enhancement before quenching . Passive galaxies have instead red colors , EW ( H \beta ) < 2.8 Å , ages in the range 9.2 < \log ( LWA [ yr ] ) < 10 . Finally , the other galaxies are most likely in transition between a post starforming and passive phase , as they quenched in an intermediate epoch and have not lost all the star forming features yet . The outside-in quenching , the morphology and kinematics of the stellar component , along with the position of these galaxies within massive clusters ( \sigma _ { cl } = 550-950 km s ^ { -1 } ) point to a scenario in which ram pressure stripping has removed the gas , leading to quenching . Only the three most massive galaxies might alternatively have entered the clusters already quenched . These galaxies are therefore at the final stage of the rapid evolution galaxies undergo when they enter the cluster environment .