The passage of molecules through membranes is known to follow an Arrhenius-like kinetics, i.e. the flux is accelerated upon heating and vice versa. There exist though stepwise processes whose rates can decrease with temperature if, for example, adsorbed intermediates are involved. In this study, we perform temperature-variable permeation experiments in the range from −50 to +50 °C and observe anti-Arrhenius behaviour of water and ammonia permeating in two-dimensional freestanding carbon nanomembranes (CNMs). The permeation rate of water vapour is found to decrease many-fold with warming, while the passage of ammonia molecules strongly increases when the membrane is cooled down to the dew point. Liquefaction of isobutylene shows no enhancement for its transmembrane flux which is consistent with the material's pore architecture. The effects are described by the Clausius–Clapeyron relationship and highlight the key role of gas–surface interactions in two-dimensional membranes.