We show that if a closed n-manifold M n (n ≥ 3) admits a structurally stable diffeomorphism f with an orientable expanding attractor Ω of codimension one, then M n is homotopy equivalent to the n-torus T n and is homeomorphic to T n for n = 4. Moreover, there are no nontrivial basic sets of f different from Ω. This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having codimension one orientable expanding attractors and contracting repellers on T n , n ≥ 3.