AbstractWe study harmonic functions associated to systems of stochastic differential equations of the form $$dX_t^i=A_{i1}(X_{t-})dZ_t^1+\cdots +A_{id}(X_{t-})dZ_t^d$$ d X t i = A i 1 ( X t - ) d Z t 1 + ⋯ + A id ( X t - ) d Z t d , $$i\in \{1,\dots ,d\}$$ i ∈ { 1 , ⋯ , d } , where $$Z_t^j$$ Z t j are independent one-dimensional symmetric stable processes of order $$\alpha _j\in (0,2)$$ α j ∈ ( 0 , 2 ) , $$j\in \{1,\dots ,d\}$$ j ∈ { 1 , ⋯ , d } . In this article we prove Hölder regularity of bounded harmonic functions with respect to solutions to such systems.