  In this paper we mainly investigate the Cauchy problem of some Camassa-Holm
type systems. By constructing a new auxiliary function, we present a
generalized Ovsyannikov theorem. By using this theorem and the basic properties
of Sobolev-Gevrey spaces, we prove the Gevrey regularity and analyticity of
these systems. Moreover, we obtain a lower bound of the lifespan and the
continuity of the data-to-solution map.
