We investigate the dependence of stellar population properties of galaxies on group dynamical stage for a subsample of the Yang catalog. We classify groups according to their galaxy velocity distribution into Gaussian (G) and Non-Gaussian (NG). Using two totally independent approaches, we have shown that our measurement of Gaussianity is robust and reliable. Our sample covers Yang’s groups in the redshift range 0.03 z 0.1, with mass . The new method, called Hellinger Distance, to determine whether a group has a velocity distribution Gaussian or NG is very effective in distinguishing between the two families. NG groups present halo masses higher than the G ones, confirming previous findings. Examining the skewness and kurtosis of the velocity distribution of G and NG groups, we find that faint galaxies in NG groups are mainly infalling, for the first time, into the groups. We show that considering only faint galaxies in the outskirts; those in NG groups are older and more metal-rich than those in G groups. Also, examining the Projected Phase Space of cluster galaxies, we see that bright and faint galactic systems in G groups are in dynamical equilibrium—which does not seem to be the case in NG groups. These findings suggest that NG systems have a higher infall rate, assembling more galaxies that have experienced preprocessing before entering the group.