Abstract <p>The dynamics of a nonequilibrium acoustically active gas are considered. In such a gas, sound waves become unstable due to relaxation processes, and, at the nonlinear stage of evolution, form a quasi-stationary system of shock-wave pulses propagating at a supersonic velocity from the disturbance source. Based on the numerical gas-dynamic simulation methods, it is shown that the dynamics and structure of these shock-wave pulses depend on the model of the vibrational relaxation time. If this relaxation time decreases with increase in the temperature more rapidly than a certain critical value, then conditions for the development of local thermal instability between the shock wave fronts can arise. In the domains with a high degree of nonequilibrium of the medium, the instability leads to a thermal explosion and the formation of strong shock waves with a small density jump. These shock waves do not have the property of evolutionarity, and therefore, they relax with time to a stable state corresponding to the structure of shock-wave pulses. A detailed analysis of the numerical simulation results shows that the intensity and the structure of shock-wave pulses are independent of initial disturbances, but determined only by the initial parameters of the nonequilibrium medium. Consequently, the system of shock-wave pulses is a nonlinear autowave structure. The convergence of the numerical solutions to the exact solution is investigated when the flow structure of nonequilibrium vibrationally excited gas is described in the neighborhood of the shock wave front. It is shown that there is a good agreement between the structure of shock waves obtained in the numerical models and the nonequilibrium shock adiabatic curve written in the Rankine–Hugoniot form with an additional term that takes into account the vibrational-translational energy exchange in the shocked gas over the width of the numerical front.</p>