  This paper is concerned with a multi-component Camassa-Holm system, which has
been proven to be integrable and has peakon solutions. This system includes
many one-component and two-component Camassa-Holm type systems as special
cases. In this paper, we first establish the local well-posedness and a
continuation criterion for the system, then we present several global existence
or blow-up results for two important integrable two-component subsystems. Our
obtained results cover and improve recent results in \cite{Gui,yan}.
