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.
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