Abstract: The Riemann problem for a two-dimensional 2×2 nonstrictly hyperbolic system of nonlinear conservaion laws has been solved thoroughly for any gived initial data which are constant in each quadrant. The non-classical shock waves, which are labelled as δ-shock waves, appear in some solutions. The solutions have been obtained are hot unique. Due to the specific property of the system considered, there are no rarefaction waves in solution.This paper is divided into three parts. The first part constructs Riemann solutions for initial data involving two contact discontinuities while the second considers the case for other initial data. The last part briefly discusses the non-uniqueness of the solutions.

Key words: Riemann problem, two-dimensions hyperbolic system, non-classical wave