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A two miniband model for electron transport in semiconductor superlattices that includes scattering and interminiband tunnelling is proposed. The model equations for Wigner functions in a basis spanned by Pauli matrices include electron-electron scattering in the Hartree approximation and modified Bhatnagar-Gross-Krook collision terms. For strong applied fields, balance equations for the electric field and the miniband populations are derived using a Chapman-Enskog perturbation technique. These equations are then solved numerically for a dc voltage biased superlattice. Results include self-sustained current oscillations due to repeated nucleation of electric field pulses at the injecting contact region and their motion toward the collector. Numerical reconstruction of the Wigner functions shows that the miniband with higher energy is empty during most of the oscillation period: it becomes populated only when the local electric field (corresponding to the passing pulse) is sufficiently large to trigger resonant tunneling.