Phase equilibria for mixtures of a polymer and a supercritical solvent are investigated by means of Expanded Gibbs Ensemble simulations. Our results indicate that such systems exhibit both lower and upper critical solution temperature (LCST and UCST) phenomena. Closed-loop miscibility diagrams are observed for systems with no specific preferences for like and unlike components. The results of our simulations for Lennard-Jones polymer-solvent mixtures are in qualitative agreement with experimental data for polymers in supercritical solvents. (C) 1998 Elsevier Science B.V. All rights reserved.