A new algorithm to find the saturation conditions of a pure substance or mixture of specified entropy is proposed. An interesting aspect is that the type of saturation point, whether a dew or bubble point, is a priori unknown. This poses particular challenges to providing good initial estimates that ensure numerical convergence of the phase equilibrium equations. A safe initialization procedure is proposed. The examples show applications of the model to computations with pure methane, pure carbon dioxide, natural gas, and contaminated carbon dioxide. The algorithm succeeds in determining the saturation condition in all of these cases. (C) 2010 Elsevier B.V. All rights reserved.