A number of models is analyzed to study gas exchange between blood capillaries and air capillaries in the avian parabronchial wall when diffusion is the only transport mechanism in the air capillaries. The existing anatomical arrangement of blood capillaries that traverse the periparabronchial tissue from peripherally located arterioles to draining venules at the luminal surface appears to provide a particularly high gas exchange efficiency. Application of the theory to measurements in the hen using histological estimates suggests that substantial concentration gradients exist inside the air capillary gas whose magnitude vary along the parabronchus. Thus at the gas inflow end of the parabronchus the partial pressure drop within the air capillaries could amount, for both O2 and CO2, to about 10--15 torr at rest and to 30--40 torr during exercise. Due to the peculiar arrangement of capillary blood flow to the air capillaries the effects of these gradients on gas exchange are very slight during rest. During exercise, however, the diffusional resistance inside the air capillaries may become limiting for the over-all gas exchange, and other mechanisms may be needed to secure respiratory gas transfer.