In this paper, we consider some experimental implications of a theory [Mol. Phys. 25, 713 (1973)] of vibrational relaxation of a guest molecule in a host matrix induced by multiphonon processes. We have explored the dependence of the vibrational relaxation rate on the guest molecular frequency, on the temperature, on the gross features of the spectrum of a monatomic and a polyatomic host matrix, and on the presence of molecular impurities. The recent experimental results of Legay, Abouaf-Marguin, and Dubost on the vibrational relaxation of CO in solid rare gases and of the 970 cm-1 vibration of NH3 in solid nitrogen are adequately interpreted in terms of the present theory.