ABSTRACT We analyse the dependence of galaxy evolution on cluster dynamical state and galaxy luminosity for a sample of 146 galaxy clusters from the Yang SDSS catalogue. Clusters were split according to their velocity distribution in Gaussians (G) and Non-Gaussians (NG), and further divided by luminosity regime. We performed a classification in the plane of mean stellar age versus specific star formation rate, providing three classes: star-forming (SF), passive (PAS) and intermediate (GV – green valley). We show that galaxies evolve in the same way in G and NG systems, but also suggest that their formation histories lead to different mixtures of galactic types and infall patterns. Separating the GV into star-forming and passive components, we find more bright galaxies in the passive mode of NG systems than in that of G systems. We also find more intermediate faint galaxies in the star-forming component of NG systems than in that of G systems. Our results suggest that GV is the stage where the transition from types Sab and Scd to S0 must be taking place, but the conversion between morphological types is independent of the dynamical stage of the clusters. Analysing the velocity dispersion profiles, we find that objects recently infalling onto clusters have a different composition between G and NG systems. While all galaxy types infall on to G systems, Sab and Scd dominate the infall on to NG systems. Finally, we find that faint Scd galaxies in the outskirts of NG systems present higher asymmetries relative to the mean asymmetry of field galaxies, suggesting that there are environmental effects acting on these objects.