The following process steps are carried out in order to purify a liquid by membrane distillation, in particular to produce desalinated water from seawater or brackish water or process water:passing a relatively warn vaporising stream of liquid (retentate stream) over a porous membrane, vapour flowing via the pores of the membrane to the other side of said membrane, andcondensing said vapour on a relatively cool condenser surface to give a distillate stream, said condenser surface forming the non-porous separation between a feed stream to be purified and said distillate steam, which feed stream is in counter-current with the retentate stream so that an appreciable proportion of the latent heat will be transferred via vapour to the feed stream, and a gas gap with a width of less than 5 mm being present between the porous membrane and the condenser surface.In order to improve the distillate flow rate per unit driving force, a pressure which is lower than the atmospheric pressure and higher than the vapor pressure of the feed stream is maintained in the gas gap, the porosity epsilon of the porous membrane is higher than 0.7, porosity being understood to be the ratio of the open volume to the total volume of the porous membrane, the surface area of the condenser surface is 1.2 to 6 times, preferably 2 to 3 times, the surface area of the porous membrane, the effective local vapour pressure difference between the retentate seam and the condensing stream is less than 10 kPa (0.1 bar), preferably less than 5 kPa (0.05 bar) and the perceptible heat of the distillate stream is released by heat exchange to the feed stream and/or the retentate stream, with preference for the retentate stream.