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

On the Martingale Problem and Feller and Strong Feller Properties for Weakly Coupled L\'evy Type Operators