By means of chemo-photometric models for galaxies of different morphological types, we have carried out a detailed study of the history of element production by spheroidal and dwarf irregular galaxies. Spheroidal galaxies suffer a strong and intense star formation episode at early times. In dwarf irregulars, the star formation rate (SFR) proceeds at a low regime but continuously. Both galactic types enrich the intergalactic medium (IGM) with metals by means of galactic winds. We have assumed that the galaxy number density is fixed and normalized to the value of the optical luminosity function observed in the local Universe. Our models allow us to investigate in detail how the metal fractions locked up in stars in spheroids and dwarf irregulars, those present in the interstellar medium (ISM) and those ejected into the IGM have changed with cosmic time. By relaxing the instantaneous recycling approximation and taking into account stellar lifetimes, for the first time we have studied the evolution of the chemical abundance ratios in the IGM and compared our predictions with a set of observations by various authors. Our results indicate that the bulk of the IGM enrichment is due to spheroids, with dwarf irregular galaxies playing a negligible role. Our predictions grossly account for the [O/H] observed in the IGM at high redshift, but overestimate the [C/H]. Furthermore, it appears hard to reproduce the abundance ratios observed in the high-redshift IGM. Some possible explanations are discussed in the text. This is the first attempt to study the abundance ratios in the IGM by means of detailed chemical evolution models which take into account the stellar lifetimes. Numerical simulations adopting our chemical evolution prescriptions could be useful to improve our understanding of the IGM chemical enrichment.