We discuss the conceptual differences between a nonequilibrium absolute temperature (defined as the partial derivative of the steady-state nonequilibrium entropy) and the local-equilibrium absolute temperature. We explore two situations in which this difference could be observed in molecular-dynamical situations. By using a simple model for the nonequilibrium entropy, we compute the difference between both temperatures for gases, metals, and electromagnetic radiation. We analyze the compatibility of both temperatures in two simple examples in the kinetic theory of gases and in an information-theoretic analysis of harmonic chains. Finally, we compare with some other works which have proposed non- equilibrium temperatures on several different grounds. © 1994 The American Physical Society.