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Relationships for the volume dependence of the Grüneisen parameter γ have been used to discuss the behaviour of solids in the limit of infinite pressure (P→∞). The model recently developed by Burakovsky and Preston (J. Phys. Chem. Solids 65 (2004) 1581) yields γ_∞, q_∞ and λ_∞, the values of Grüneisen parameter γ and its logarithmic volume derivatives q and λ at P→∞, which are found to have fixed values, same for all the solids studied. On the other hand, the thermodynamics of solids at P→∞ formulated by Stacey (Geophys. J. Int. 143 (2000) 621) reveals that γ_∞ and pressure derivative of bulk modulus [Formula: see text] are different for different materials. The empirical formulation for the volume dependence of γ used by Stacey and Davis (Phys. Earth Planet. Intr. 142 (2004) 137) has been shown to be approximately equivalent to the relationship proposed earlier by Al’tshuler et al. (J. Appl. Mech. Tech …