The ascent of Mt. Everest (altitude 8848 m) by two climbers in May 1978 without supplementary oxygen has prompted us to make a theoretical analysis of gas exchange under these conditions of extreme hypoxia. On the basis of previous measurements made up to an altitude of 7440 m and other data, we have calculated a barometric pressure on the summit of 250 Torr, alveolar PCO2 of 10 Torr, and Hb concentration of 20.5 g/100 ml. Values for cardiac output, pulmonary capillary blood volume, and diffusing capacity were based on measurements made at 5800 m. A striking result of calculations of oxygenation along the pulmonary capillary is that, even at rest, there is an alveolar-end capillary PO2 of about 6 Torr caused by diffusion limitation, and this widens rapidly on mild exercise. Arterial and mixed venous PO2 fall precipitously as the VO2 is raised further. If we assume that the PO2 in mixed venous blood cannot fall below 15 Torr, a maximal VO2 of less than 700 ml/min is predicted. Arterial O2 saturation and, to a smaller extent, the mixed venous PO2 can be increased by shifting the O2 dissociation curve to the left. This can be accomplished by fully compensating for the respiratory alkalosis at a lower altitude, and then climbing rapidly to the summit. Maximal VO2 is extremely sensitive to barometric pressure, and to a lesser extent to lung diffusing capacity. The results are in general agreement with extrapolations from measurements of maximal VO2 at altitudes up to 7440 m.