Resting or basal metabolic rates, compared across a wide range of organisms, scale with respect to body mass as approximately the 0.75 power. This relationship has recently been linked to the fractal geometry of the appropriate transport system or, in the case of birds and mammals, the blood vascular system. However, the structural features of the blood vascular system should more closely reflect maximal aerobic metabolic rates rather than submaximal function. Thus, the maximal aerobic metabolic rates of birds and mammals should also scale as approximately the 0.75 power. A review of the literature on maximal oxygen consumption and factorial aerobic scope (maximum oxygen consumption divided by basal metabolic rate) suggests that body mass influences the capacity of the cardiovascular system to raise metabolic rates above those at rest. The results show that the maximum sustainable metabolic rates of both birds and mammals are similar and scale as approximately the 0.88 +/- 0.02 power of body mass (and aerobic scope as approximately the 0.15 +/- 0.05 power), when the measurements are standardized with respect to the differences in relative heart mass and haemoglobin concentration between species. The maximum heart beat frequency of birds and mammals is predicted to scale as the -0.12 +/- 0.02 power of body mass, while that at rest should scale as -0.27 +/- 0.04.