Environmental stress can become so severe that athletes, in spite of proper training, heat acclimation, and hydration level, are unable to maintain thermal balance. Such incompensable conditions occur when air temperature exceeds 35 degrees C and relative humidity becomes higher than 60%. At these high environmental temperatures, the heat liberated during exercise can only be lost by evaporation of sweat, and therefore water vapor pressure sets limits on the possible rate of evaporation. Calculations are presented for the required and the maximal possible sweat evaporation rate for high-intensity, long-duration events, using marathon racing as an example. The consequence of the environmental heat stress is that the athlete must reduce the speed of running considerably to prevent potential heat injury. In certain extreme environmental conditions, sporting events should be canceled or postponed.