  We present a new class of hydrodynamical models for the formation of bulges
(either massive elliptical galaxies or classical bulges in spirals) in which we
implement detailed prescriptions for the chemical evolution of H, He, O and Fe.
Our results hint toward an outside-in formation in the context of the
supernovae-driven wind scenario. The build-up of the chemical properties of the
stellar populations inhabiting the galactic core is very fast. Therefore we
predict a non significant evolution of both the mass-metallicity and the
mass-[alpha/Fe] relations after the first 0.5 - 1 Gyr. In this framework we
explain how the observed slopes, either positive or negative, in the radial
gradient of the mean stellar [alpha/Fe], and their apparent lack of any
correlation with all the other observables, can arise as a consequence of the
interplay between star formation and metal-enhanced internal gas flows.
