Process for separating a gas or liquid mixture by means of a separating device comprising a first volume (V1) and a second volume (V2) separated by a membrane (MS) having a selective permeability relative to at least two components of said mixture, the process comprising steps consisting in: a) filling the first volume of the device with the mixture (M1) to be separated; b) waiting a length of time (t2-ti) longer than the permeation lag time, but insufficient for an equilibrium state to be reached, during which time a fraction of each component of said mixture passes from the first to the second volume of the device through the membrane; c) evacuating the first and second device volume in order to obtain at least one first (R) and one second (P, P1, P2) cut of the mixture, having different molar compositions.