Summary: This paper studies the dynamical stability of the steady state for some thermoelastic and thermoviscoelastic systems in a multi-dimensional space domain. Here, a more general nonlinear term than the one in [I. Pawłow, Control Cybern. 29, No. 1, 341–365 (2000; Zbl 1205.74140)] is used which studied the stability for the one-dimensional system called the Falk model system. We also give applications to thermoviscoelastic systems treated in [the second author, I. Pawłow and W. M. Zajączkowski, SIAM J. Math. Anal. 38, No. 6, 1733–1759 (2007; Zbl 1131.35083); Commun. Pure Appl. Anal. 8, No. 3, 1093–1115 (2009; Zbl 1160.74017)].