A membrane distillation process carried out in a system comprising a plurality of modules, which method comprises the steps of: - applying an underpressure to at least one of the modules of the system, which underpressure is forwarded to other modules through pressure communication; - generating a vapour flow in a steam generator, that flows into a heating channel; - generating distillate from a feed by means of evaporation to vapour in a first liquid channel of a membrane distillation module (14, 16), which vapour is removed through a membrane and subsequently condensed in a vapour channel, wherein heat transfer occurs from the vapour channel to any subsequent liquid channel, and wherein the evaporation of feed in the first liquid channel occurs upon heat transfer from the heating channel in which the vapour flow condenses: - repeatedly, in dependence of the number of distillation modules (14, 16) in use, transferring non-evaporated feed of the preceding membrane distillation module (14, 16) to a subsequent membrane distillation module (14, 16), and generating distillate from vapour passed into a subsequent vapour channel, therewith transferring heat to an adjacent liquid channel, and - generating the distillate of the last membrane distillation module in a vapour channel of a condenser module against a cooling fluid running in a cooling channel of the condenser module, characterized in that the method further comprises the steps of: - supplying a multi-phase feed to the steam generator, which multi-phase feed comprises a liquid phase and a vapour phase as a mixture; - removing a mixture predominantly comprising vapour from the multi-phase feed, which mixture is further evaporated to generate the vapour flow, and - transferring the multi-phase feed remaining after the removal step to the first liquid channel for use as the feed. - applying an underpressure to at least one of the modules of the system, which underpressure is forwarded to other modules through pressure communication; - generating a vapour flow in a steam generator, that flows into a heating channel; - generating distillate from a feed by means of evaporation to vapour in a first liquid channel of a membrane distillation module (14, 16), which vapour is removed through a membrane and subsequently condensed in a vapour channel, wherein heat transfer occurs from the vapour channel to any subsequent liquid channel, and wherein the evaporation of feed in the first liquid channel occurs upon heat transfer from the heating channel in which the vapour flow condenses: - repeatedly, in dependence of the number of distillation modules (14, 16) in use, transferring non-evaporated feed of the preceding membrane distillation module (14, 16) to a subsequent membrane distillation module (14, 16), and generating distillate from vapour passed into a subsequent vapour channel, therewith transferring heat to an adjacent liquid channel, and - generating the distillate of the last membrane distillation module in a vapour channel of a condenser module against a cooling fluid running in a cooling channel of the condenser module, - supplying a multi-phase feed to the steam generator, which multi-phase feed comprises a liquid phase and a vapour phase as a mixture; - removing a mixture predominantly comprising vapour from the multi-phase feed, which mixture is further evaporated to generate the vapour flow, and - transferring the multi-phase feed remaining after the removal step to the first liquid channel for use as the feed.