The van der Waals and Platteeuw [Adv. Chem. Phys. 2 (1959) 1] hydrate equation of state, coupled with the classical thermodynamic equation for hydrates, has been used in the prediction of hydrate formation for over 40 years. The standard state used in these equations is a hypothetical empty hydrate lattice. In Part I of this series [Fluid Phase Equilib. 194-197 (2002) 37 1], we proposed an alternative derivation of these equations using a different standard state. The new hydrate equations were shown to be simpler to use. In Part H of this series [Fluid Phase Equilib. 211 (2003) 85], we proposed an aqueous phase model tailored specifically for the presence of mixed hydrate inhibitors such as salts and methanol in the aqueous phase. Part III provides a prescription for the incorporation of the new hydrate and aqueous phase models into a multi-phase Gibbs energy minimization program (CSMGem). This paper extends the work of Bishnoi et al. [Fluid Phase Equilib. 53 (1989) 97] to apply a Gibbs energy minimization routine to several phases of interest and perform multi-phase flashes. In this work, we account for the aqueous, ice, solid salts, vapor, liquid hydrocarbon, sI hydrate, sII hydrate, and sH hydrate phases. The work is intended to clarify the algorithm and equations for Gibbs energy minimization. We discuss implementation of the Gibbs energy minimization, incorporation of all phases, initialization of the algorithm, and the treatment of hydrate phases in the calculation. Due to the highly non-ideal behavior of the hydrate phase, several precautions must be taken to ensure convergence. Since the method is not restricted to hydrate calculations, and because there is a scarcity of such code, a World Wide Web link to the Gibbs energy minimization source code is provided. (C) 2003 Elsevier B.V. All rights reserved.