  We study the mass-metallicity relation of galactic systems with stellar
masses larger than 10^9 Mo in Lambda-CDM scenarios by using chemical
hydrodynamical simulations. We find that this relation arises naturally as a
consequence of the formation of the structure in a hierarchical scenario. The
hierarchical building up of the structure determines a characteristic stellar
mass at M_c ~10^10.2 Moh^-1 which exhibits approximately solar metallicities
from z ~ 3 to z=0. This characteristic mass separates galactic systems in two
groups with massive ones forming most of their stars and metals at high
redshift. We find evolution in the zero point and slope of the mass-metallicity
relation driven mainly by the low mass systems which exhibit the larger
variations in the chemical properties. Although stellar mass and circular
velocity are directly related, the correlation between circular velocity and
metallicity shows a larger evolution with redshift making this relation more
appropriate to confront models and observations. The dispersion found in both
relations is a function of the stellar mass and reflects the different
dynamical history of evolution of the systems.
