<p>This paper investigates the time asymptotic stability of composite waves formed by two shock waves within the context of one-dimensional relaxed compressible Navier-Stokes equations. We establish the nonlinear stability of the composite waves consisting of two viscous shocks under the condition of having two small, independent wave strengths and the presence of small initial perturbations. Furthermore, the solutions of the relaxed system are observed to globally converge over time to those of the classical system as the relaxation parameter approaches zero. The methods are based on relative entropy, the <i>a</i>-contraction with shifts theory and fundamental energy estimates.</p>