The determination of the composition of multi-component mixtures is the basis by which a number of technical and physical problems in the field of power and process engineering are modelled. In order to calculate chemical states of equilibrium in the gas phase, a calculation method will be presented which is founded on a minimization of the Gibbs enthalpy. This method is characterized by a high reliability in convergency, considerable independence of starting vectors and by a moderate requirement for programming. These characteristics are achieved by a transformation of variables which results in numerically more favourable solutions to the non-linear equation system. Calculated equilibrium compositions (including dissociation and ionisation) for a stochiometric mixture of hydrogen and oxygen in a temperature range of 300 -12 000 K and a pressure of 10(5) Pa as well as the application of the method will be demonstrated.