The invention defines a device for the separation of fluid mixtures, comprising one or several membranes, in which the fluid mixture passes along one side of the membranes while, on the other side, a partial pressure of the constituent to be separated is maintained which is lower than the pressure in the fluid mixture.The inventive device is characterized by the fact that at least one heatable membrane is provided. The selective (separating) portion of the membrane may be a porous or a pervaporation membrane.The membrane may also comprise a supporting structure in addition to the selective portion, which may be made of a porous material in a preferred embodiment.Another preferred embodiment comprises a membrane coated with a material which is preferably wetted by the constituent to be separated by the respective membrane.