We study harmonic functions associated to systems of stochastic differential equations of the form dXi t = Ai1( Xt-)dZ1 t + center dot center dot center dot + Aid (Xt-)dZd t, i. {1,..., d}, where Z j t are independent one-dimensional symmetric stable processes of order aj. (0, 2), j. {1,..., d}. In this article we prove Holder regularity of bounded harmonic functions with respect to solutions to such systems.