  This paper is concerned with global existence and blow-up phenomena for
two-component Degasperis-Procesi system and two-component b-family system. The
strategy relies on our observation on new conservative quantities of these
systems. Several new global existence results and a new blowup result of strong
solutions to the two-component Degasperis- Procesi system and the two-component
b-family system are presented by using these new conservative quantities.
