  We consider actions of Z^k, k \ge 2, by Anosov diffeomorphisms which are
uniformly quasiconformal on each coarse Lyapunov distribution. These actions
generalize Cartan actions for which coarse Lyapunov distributions are
one-dimensional. We show that, under certain non-resonance assumptions on the
Lyapunov exponents, a finite cover of such an action is smoothly conjugate to
an action by toral automorphisms.
