By means of chemical evolution models for galaxies of different morphological types (i.e. spirals and irregular/starburst galaxies) we study the nature of Damped Lyman-alpha (DLA) systems. By focusing on individual systems, we can derive important constraints on both their star formation history and their age. Our results indicate that the local conterparts of most DLAs are represented by dwarf galaxies having had low star formation rates, but some systems can also be associated to spirals. Some systems are already old, with ages of ∼1 Gyr, and some others are experiencing the very first star formation episodes.