We study the evolution of the cosmic star formation by computing the luminosity density (LD) in the UV, B, J, and K bands, and the stellar mass density (MD) of galaxies in two reference models of galaxy evolution: the pure luminosity evolution (PLE) model developed by Calura & Matteucci (2003) and the semi-analytical model (SAM) of hierarchical galaxy formation by Menci et al. (2002). The former includes a detailed description of the chemical evolution of galaxies of different morphological types with no density evolution; the latter includes the merging histories of the galactic DM haloes, as predicted by the hierarchical clustering scenario, but it does not contain morphological classification nor chemical evolution. We find that at z< 1.5 both models are consistent with the available data on the LD of galaxies in all the considered bands. At high z, the LDs predicted in the PLE model show a peak due to the formation of ellipticals, whereas the SAM predicts a gradual decrease of the star formation and of the LD for z> 2.5. At such redshifts the PLE predictions tend to overestimate the present data in the B band whereas the SAM tends to underestimate the observed UV LD. As for the stellar MD, the PLE picture predicts that nearly 50% and 85% of the present stellar mass are in place at z=4 and z=1, respectively. According to the SAM, 50% and 60% of the present stellar mass are in place at z=1.2 and z=1, respectively. Both predictions fit the observed MD up to z=1. At z>1, the PLE model and the SAM tend to overestimate and underestimate the observed values, respectively. We discuss the origin of the above model results, and the role of observational uncertainties (such as dust extinction) in comparing models with observations. Comment: 14 pages, accepted for publication in MNRAS