In this communication, we analyse the passage of oxygen and carbon dioxide over the respiratory membrane. The lung surfactant membrane at the alveolar interface can have a very special arrangement, which affects the diffusional transport. We present a theoretical model for the diffusion of small molecules in membranes with a complex structure, and we specifically compare a membrane composed of a tubular bilayer network with a membrane consisting of a stack of bilayers. Oxygen and carbon dioxide differ in terms of their solubility in the aqueous and the lipid regions of the membrane, and we show that this difference clearly influences their transport properties in the different membrane structures. During normal respiration, the rate-limiting step for carbon dioxide transport is in the gas phase of the different compartments in the lung. For oxygen, on the other hand, the rate is limited by the transport between alveoli and the capillary blood vessels, including the lung surfactant membrane. In a membrane with a structure of a continuous tubular lipid network, oxygen transport is facilitated to a significant extent compared with the structure of aligned lipid bilayers. The model calculations in the present study show that transport of oxygen through the tubular structure is indeed ca 30 per cent faster than transport through a membrane composed of stacked bilayers. The tubular network will also facilitate the transport of apolar substances between the gas phase and the blood. Important examples are ethanol and other volatile liquids that can leave the blood through the lungs, and gaseous anaesthetics or volatile solvents that are inhaled. This exemplifies a new physiological role of a tubular lipid network in the lung surfactant membrane.