The antiferromagnetic ion-ion interactions observed in A(II)B(VI) dilu
ted magnetic semiconductors (DMS) impose an upper limit to the increas
e of the giant free carrier spin-splitting with the growing content of
the magnetic ions. In this paper we report the first calculations of
the superexchange in Cr-based DMS and we predict the ion-ion interacti
ons to be ferromagnetic in these materials. Within the same model we c
larify the origins of the recently discovered ferromagnetic p-d intera
ctions in zinc chalcogenides with Cr2+ paramagnetic ions.