We revisit the bimodality of the galaxy population seen in the local universe. We address this issue in terms of physical properties of galaxies, such as mean stellar ages and stellar masses, derived from the application of a spectral synthesis method to galaxy spectra from the SDSS. We show that the mean light-weighted stellar age of galaxies presents the best description of the bimodality seen in the galaxy population. The stellar mass has an additional role since most of the star-forming galaxies present in the local universe are low-mass galaxies. Our results give support to the existence of a ‘downsizing’ in galaxy formation, where nowadays massive galaxies tend to have stellar populations older than those found in less massive objects.