No extensive investigations of the phase equilibria of complex mixtures at low temperatures and high pressures have hitherto been reported. In the present paper the coal-gas system has been studied, the apparatus employed by Ruhemann for the study of the vapour-liquid equilibria in binary mixtures has been modified and is described in detail. The pressure-composition curve of methane-ethylene mixtures has been determined at - 104 degrees C and is compared with the available data. Tables of experimental compositions of the equilibrium phases at - 104, -160$\cdot $6, - 183 and -195$\cdot $5 degrees C are given for the complex system-coal gas -at pressures up to 90 atm. Material balance calculation based on each component is used to check accuracy of the equilibrium determinations for complex mixtures. The amount of solids formed in the condensed phase at -195$\cdot $5 degrees C is roughly estimated. A method for calculating the composition of the condensed phase from the analysis of the equilibrium vapour phase and of original gas is outlined. The pressure-composition isotherms for the hydrogen component are reproduced; the temperature-composition isobars up to 25 atm. are also derived. The relationship between phase properties for the hydrogen component in the binary and the complex systems is discussed. A method for predicting the phase behaviour of the complex mixture studied is described; the application of this method to coke-oven gas is illustrated. The utilization of the experimental data obtained for the design of plant is briefly discussed.