  In this paper, the successive approximation method is applied to investigate
the existence and uniqueness of solutions to the stochastic differential
equations (SDEs) driven by L\'evy noise under non-Lipschitz condition which is
a much weaker condition than Lipschiz one. The stability of the solutions to
non-Lipschitz SDEs driven by L\'evy noise is also considered, and the
stochastic stability is obtained in the sense of mean square.
