Using current models of spectrophotometric properties of single age, single metallicity and stellar populations (SSPs) I have computed the Mg-2, H beta, Fe52 and Fe53 line strengths for stellar populations with a metallicity spread. The comparison of these models with the nuclear indices of early-type galaxies yields the following major conclusions. The metallicity distribution of the closed box, simple model for the chemical evolution of galaxies is not able to account for Mg, and Fe52, Fe53 values in excess of similar to 0.27, 3 and 2.7, respectively, which are observed in the nuclei of a large fraction of ellipticals. To reproduce the line strengths in these galaxies high average metallicities, small metallicity dispersion and high ages are required. In particular, Mg-2 values of similar to 0.3 are reproduced only with a metallicity distribution ranging from similar to 0.5 to similar to 3 Z(circle dot), and similar to 15 Gyr old stellar populations. I interpret the data as indicating that the gas out of which the nuclei of ellipticals formed was pre-enriched, to larger metallicities for increasing Mg,. The presence of a metallicity dispersion does not alter the relation between Mg, and iron indices with respect to the SSP models. Thus, the need for a Mg/Fe overabundance in the strongest lined galaxies is con firmed, and I present a simple way to estimate the [Mg/Fe] ratio on the basis of existing models with solar abundance ratios.