||In this talk we consider some hyperbolic systems of balance laws. The generalized Glimm scheme is introduced to establish the global existence of existence of weak solutions for the initial and initial-boundary value problems of those systems. The dissipative conditions are derived to control the bound of total variation of approximate solution so that the stability
of the generalized Glimm scheme can be obtained. This is the joint work with Shih-Wei Chou of National Central University and Ying-Chin Su of Fu Jen Catholic University.