Abstract: The aim of this paper is to discuss the existence of global BV solutions for a class of systems of quasilinear hyperbolic equ ations with Radon measures as initial conditions. We firstly considered its regularized problem. With the aid of a series of critical analysis and by a limit process, we obtained the existence of global solutions for the regularized problem. In particular, we also obtained the uniform BV estimates for it. Then again, by a limit process, the existence of global BV solutions for the original problem was obtained.

Key words: systems of quasilinear hyperbolic, Cauchy problem, exi stence