Gas transfer in membrane oxygenators can be limited by the liquid dispersion or the membrane diffusion. If limited by liquid dispersion, the increase in average oxygen saturation of blood flowing in straight gas-permeable tubes is dependent upon the flow rate, the tube length, and the diffusion coefficient and independent of the tube diameter. The mathematical solution is surprisingly insensitive to shifts of the oxyhemoglobin dissociation curve. The assumptions utilized in the model and the analytic solution were verified by a series of experiments using cattle blood. Tube staging, turbulence, and tube coiling bring about mixing and significantly improve the oxygenation rate. For coiled tubes, the oxygenation efficiency depends on the Reynolds number, the Schmidt number, and the tightness of the coil. The limit on the rate of oxygen addition and carbon dioxide removal might be imposed, for thick-walled tubes, by the diffusion through the tube wall. The wall-limited case is governed by CO2 removal. © 1969 International Federation for Medical and Biological Engineering.