The unlike interaction parameters for binary mixtures of helium + non-polar gases are obtained by comparing experimental critical data with calculations using the Guggenheim and Heilig-Franck equations of state. These interaction parameters and equations of state are used to predict a priori both the vapour-liquid and liquid-liquid equilibria for helium + non-polar gas mixtures. The predicted phase diagrams are compared with experimental data for a wide range of pressure, temperature and composition. Good agreement between theory and experiment is obtained for the isobaric temperature-composition phase behaviour and isothermal pressure-composition phenomena can be predicted qualitatively.