Abstract: We studied the existence of the global smooth solutions for degenerate Gourset problem of a class of hyperbolic conversation law systems. Firstly, we introduced  characteristic angles α,β, and established characteristic decompositions for α,β and pressure 
P. Secondly, the characteristic decompositions of  α,β were used to obtain the invariant region, and then the maximum norm estimate of the characteristic angles were obtained. Finally, the gradient estimates of the solution were established by the characteristic decomposition of pressure P and continuity method, which proved the existence of the solutions to the degenerate Gourset problem.

Key words: hyperbolic conservation law system, characteristic decomposition, degenerate Goursat problem, planar rarefaction wave