  This work focuses on a class of regime-switching jump diffusion processes,
which is a two component Markov processes $(X(t),\Lambda(t))$, where
$\Lambda(t)$ is a component representing discrete events taking values in a
countably infinite set. Considering the corresponding stochastic differential
equations, our main focus is on treating those with non-Lipschitz coefficients.
  We first show that there exists a unique strong solution to the corresponding
stochastic differential equation. Then Feller and strong Feller properties are
investigated.
