An overall strategy for phase equilibrium calculations within chemically reacting multicomponent nonideal systems is presented. The strategy involves three stages and employs an indirect method to determine the phase configuration of the reacting system at equilibrium. The latter is based on an existing technique for the solution of the phase equilibrium problem extended tu include chemically reacting systems, Independently, a new algorithm for chemical equilibrium calculations in any prescribed number of phases is advocated. A detailed analysis of its computational efficiency on the basis of multiplication operations required is provided. Results for three chemically reacting systems, two of which exhibit complex phase equilibria, are given and compared with the results of other authors.