Abstract In this paper, we focus on ram-pressure stripping and evaporation of disk galaxies in and around a cluster. We show that the evolution of the disk surface density affects the efficiency of ram-pressure stripping of galaxies at $z\gtrsim 1$. We also consider the saturation of thermal conduction in detail and show that it cannot be ignored at larger radii of a cluster, which makes the time-scale of the evaporation larger. Both the ram-pressure stripping and evaporation could affect the evolution of galaxies even around a cluster. In particular, the observed gradual decline of the star-formation rates of galaxies in and around clusters could be explained by evaporation without resorting to speculative strangulation (stripping of warm gas in galactic halos).