<p>The time-asymptotic stability for one-dimensional relaxed compressible Navier-Stokes equations is studied. We show that the composite waves, consisting of viscous shock and rarefaction, exhibit asymptotic nonlinear stability under conditions of small wave strength and initial perturbations. Furthermore, as the relaxation parameter approaches zero, the solutions of the relaxed system are shown to globally converge over time to those of classical system. Our approach relies on relative entropy, the a-contraction with shifts theory, and fundamental energy estimates.</p>