The two nearest, best-studied groups of galaxies, the Local Group and the M81 group, are analyzed. It is shown that 22 out of 22 major companions have redshifts that are positive with respect to the dominant galaxy. The chance that this can be an accidental configuration of velocities is only one in four million. Investigations of more distant groups, including clusters such as Virgo, show that the smaller galaxies characteristically have systematically positive redshifts with respect to the larger ones. No selection effects or contamination are capable of avoiding this result. The ''Fingers of God'' seen in wedge diagrams of galaxies are shown to give additional evidence against the velocity interpretation of redshifts. Spectra, color, and morphology agree in identifying evolutionary age as the parameter correlated with the excess redshift of the companions.