  Using a slave boson representation of multi-band Hubbard models, we
investigate a two-band model relevant to layered perovskites in the vicinity of
half-filling. Beside the strong influence of the Hund's rule coupling, we
obtain that the phase diagram separates into two regions: a weak to moderate
coupling region where the effective mass is weakly renormalized, and a strong
coupling regime where it is strongly renormalized. The transition between these
two regimes is very sharp. It takes place in a (vanishingly) small domain. A
ferromagnetic instability in only found in the strongly correlated regime, and
is triggered by the Hund's rule coupling. The results are compared to La-doped
layered ruthenates.
