Abstract: A process for distilling multicomponent hydrocarbon mixtures in which the relative volatility between the dominant component in the lightest product and the dominant component in the heaviest component is between 1.10 and 7. The hydrocarbon mixture is fed to groups of distillation columns each of which is provided with an overhead condenser and a bottom reboiler, the columns being arranged in succession to receive the product from the prior adjacent column. The operating pressure in the columns increases from the first column to the final column within prescribed limits and the products of the mixture are separately recovered at one time in the final column without being withdrawn from intermediate distillation columns. Heat is recovered from heat source streams of the process by heat exchange with heat sink streams by bringing the streams successively in contact with a plurality of groups of heat exchangers, each group being at a different temperature level.