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A generalized Ruderman-Kittel-Kasuya-Yosida (RKKY) approach is used to calculate indirect exchange interactions between localized spins in doped magnetic semiconductors. The exchange is mediated by electron or hole states centered around shallow impurities. The states hybridize and may or may not form a narrow band, but in both cases, the exchange is obtained from the hybridized states by second-order perturbation theory. As in the free-electron RKKY model, both positive and negative exchange interactions occur, but the strength Jij of the exchange is no longer a unique function of the distance between the localized spins. A closed expression with simple geometric interpretation is obtained in the dilute limit of exchange mediated by two overlapping orbitals.