  This paper considers the martingale problem for a class of weakly coupled
L\'{e}vy type operators. It is shown that under some mild conditions, the
martingale problem is well-posed and uniquely determines a strong Markov
process $(X,\Lambda)$. The process $(X,\Lambda)$, called a regime-switching
jump diffusion with L\'evy type jumps, is further shown to posses Feller and
strong Feller properties under non-Lipschitz conditions via the coupling
method.
