By means of detailed chemical evolution models for galaxies of different morphological types (i.e. spirals, irregular/starburst galaxies and ellipticals) we study the nature of Damped Lyman-Alpha systems. Our concern is to infer which systems represent likely candidates for the DLA population and which do not. By focusing on individual systems, we can derive some constraints on both the nature of the associated galaxy and its age. Our results indicate that, owing to their high metallicities and [alpha/Fe] ratios, big spheroids represent unlikely DLA candidates whereas spirals (observed at different galactocentric distances) and irregulars are ideal sites where DLA absorptions can occur.