  We consider systems of stochastic differential equations of the form \[ \d
X_t^i = \sum_{j=1}^d A_{ij}(X_{t-}) \d Z_t^j\] for $i=1,\dots,d$ with
continuous, bounded and non-degenerate coefficients. Here $Z_t^1,\dots,Z_t^d$
are independent one-dimensional stable processes with
$\alpha_1,\dots,\alpha_d\in(0,2)$. In this article we research on uniqueness of
weak solutions to such systems by studying the corresponding martingale
problem. We prove the uniqueness of weak solutions in the case of diagonal
coefficient matrices.
