  Motivated by the work of P.L. Lions and J-C. Rochet [12], concerning
multi-time Hamilton-Jacobi equations, we introduce the theory of multi-time
systems of conservation laws. We show the existence and uniqueness of solution
to the Cauchy problem for a system of multi-time conservation laws with two
independent time variables in one space dimension. Our proof relies on a
suitable generalization of the Lax-Oleinik formula.
