We describe a generalization of the negative-flash method for computing the equilibrium compositions of systems that can form more than two fluid phases. We show the solution existence and uniqueness of the general Rachford-Rice problem for systems with any number of phases. A bisection based strategy is proposed either as a solution procedure to guarantee convergence, or as a preconditioning step of Newton based methods. A multi-stage negative-flash procedure is developed to identify the state of a multicomponent mixture where the maximum number of phases is arbitrary. The approach should be used in combination with a tie-simplex based modeling framework to provide a general method for phase behavior computations. Challenging numerical examples are presented to demonstrate the accuracy and robustness of the negative-flash approach. (C) 2010 Elsevier B.V. All rights reserved.