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Weakly nonlinear sound propagation in a gas where molecular vibrational relaxation takes place is studied. New equations which govern the sound in media where the irreversible relaxation may take place are derived and discussed. Their form depends on the regime of excitation of oscillatory degrees of freedom, equilibrium (reversible) or non-equilibrium (irreversible), and on the comparative frequency of the sound in relation to the inverse time of relaxation. Additional nonlinear terms increase standard nonlinearity of the high-frequency sound in the equilibrium regime of vibrational excitation and decrease otherwise. As for the nonlinearity of the low-frequency sound, the conclusions are opposite. Appearance of a non-oscillating additional part which is a linear function of the distance from the transducer is an unusual property of nonlinear distortions of harmonic at the transducer high-frequency sound
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