The influence of temperature on the vibron-phonon combination band in the Raman and infrared (ir) spectra of the N2 and O2 molecular crystals supports the possibility of an assignment of the main features in the sideband to strong contributions from translational and librational phonons in points of high symmetry in the reciprocal lattices. The temperature behavior in Raman and ir sideband spectra in alpha-N2 is attributed to distinct anharmonicities in the isotropic and anisotropic parts of the potential and to different coupling mechanisms, resulting in a librational and translational weighted one-phonon density of states (DOS). In contrast, such an interpretation is not feasible for the poorly structured CO sideband, although the crystal structures of CO and N2 are nearly identical. The difference is attributed to strong anharmonicities and the presence of a weak dipole moment in the former, which introduces strong lattrice mode coupling. Crossing the alpha-beta-phase transition has marked effects on the sidebands (shape, intensity) in both N2 and O2 crystals, which reflects the orientational disorder in the beta-phase of the former and the importance of the change in magnetic interactions in the latter. For both molecular crystals, the vibron-phonon coupling to the electromagnetic field is stronger in the ir than in the Raman spectra and seems predominantly due to electrical anharmonicities.