Abstract: A microscopic Hamiltonian for interacting manganese impurities in dilute magnetic semiconductors (DMS) is derived. It is shown that in p-type III-V DMS, the indirect exchange between Mn impurities has similarities with the Zener mechanism in transition metal oxides. Here the mobile and localized holes near the top of the valence band play the role of unoccupied p-orbitals which induce ferromagnetism. T-C estimated from the proposed kinematic exchange agrees with experiments on (Ga,Mn)As. The model is also applicable to the p-doped (Ga,Mn)P system. The magnetic ordering in n-type (Ga,Mn)N is due to exchange between the electrons localized on the levels lying deep in the forbidden energy gap. This mechanism is even closer to the original Zener mechanism. (C) 2003 Elsevier B.V. All rights reserved.