Abstract. The strong chain recurrent points and strong chain transitive sets of a homeomorphism f on a compact metric space X, first introduced by Easton, [E]. He note that, if chain recurrent set of f is all of X, then strong chain recurrent set and strong chain transitive set of f are useful. Here, we obtain some results about strong chain recurrency. In particular, we show that an isolated strong chain class S of generic homeomorphism f has a generic continuation Sg, where g close to f, in C-topology. Moreover, we have the generic persistence of Lipschitz ergodicity at f near S.

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