We consider systems of conservation laws which satisfy classical physical assumptions: Galilean invariance,reversibility of smooth solution and existence of an convex entropy.A common form can be deduced and we use it to construct general numerical schemes.They are based on a relaxation approximation,proved to be nonlinearly stable.The resulting schemes are proved to be entropy satisfying.Thanks to this property,error estimates for strong solutions and convergence towards measure-valued solutions can be obtained.