We present a study of the galaxy population predicted by hydrodynamical simulations for a set of 19 galaxy clusters based on the GADGET-2 Tree+SPH code. These simulations include gas cooling, star formation, a detailed treatment of stellar evolution and chemical enrichment, as well as SN energy feedback in the form of galactic winds. We compute the spectro-photometric properties of the simulated galaxies. All simulations have been performed for two choices of the stellar initial mass function: a standard Salpeter IMF, and a top-heavier IMF. Several of the observational properties of the galaxy population in nearby clusters are reproduced fairly well by simulations. A Salpeter IMF is successful in accounting for the slope and the normalization of the color-magnitude relation for the bulk of the galaxy population. Simulated clusters have a relation between mass and optical luminosity which generally agrees with observations, both in normalization and slope. We find that galaxies are generally bluer, younger and more star forming in the cluster outskirts, thus reproducing the observational trends. However, simulated clusters have a total number of galaxies which is significantly smaller than the observed one, falling short by about a factor 2-3. Finally, the brightest cluster galaxies are always predicted to be too massive and too blue, when compared to observations, due to gas overcooling in the core cluster regions, even in the presence of a rather efficient SN feedback. ; Comment: 15 pages, 17 figures, to appear in MNRAS