A new algorithm is proposed for calculating phase equilibria in binary systems at a fixed temperature and pressure. This algorithm is then extended to ternary systems (in which case, the mole fraction of one constituent in a given phase must be fixed in order to satisfy the Gibbs' phase rule). The algorithm has the advantage of being very simple to implement and insensitive to the procedure used to initialize the unknowns. Most significantly, the algorithm allows the same solution procedure to be used regardless of the thermodynamic approach considered (gamma-phi or phi-phi), the type of phase equilibrium (VLE, LLE, etc.) and the existence of singularities (azeotropy, criticality and so on).