<p>Thanks to the works by R. V. Plykin and V. Z. Grines, the most studied expanding attractors are orientable attractors of codimension one of <i>A</i>-diffeomorphisms of multidimensional closed manifolds and one-dimensional attractors on closed surfaces. In this paper, we prove that there exist closed manifolds of any dimension starting with three, admitting structurally stable diffeomorphisms and diffeomorphisms satisfying Smale’s axiom A, with expanding attractors of arbitrary codimension. For some codimensions the type of manifolds is obtained.</p>