The flow of isobutane and of freon 142b (1-chloro-1,1-difluoro-ethane) through anodic alumina membranes with pore diameters between 18 and 60 nm in a capillary condensation regime is experimentally and theoretically explored. The capillary condensation effect increases the membrane permeance for condensable gases from 25 to 150 m3(STP) m-2 bar-1 h-1 at certain conditions. To describe the experimental results, a model is suggested accounting for heat transfer from the condensing to the evaporating meniscus, different boundary conditions for the heat transfer between the environment and the membrane, and wettability of the pore wall. The proposed model indicates a large influence of heat supply from the environment to the membrane on the permeance in the capillary condensation regime and a moderate influence of condensate contact angle in the range of 0-60°. Measuring the temperature of the permeate side of the membrane allows to find a suitable boundary condition to describe heat transfer. The obtained boundary condition yields an excellent fit of experimental results of condensate flow through membranes with different pore diameters for the two utilized fluids. Also, confocal Raman spectroscopy gave evidence on the fraction of pores filled with condensate.