1. At high running speeds, the step frequency becomes lower than the apparent natural frequency of the body's bouncing system. This is due to a relative increase of the vertical component of the muscular push and requires a greater power to maintain the motion of the centre of gravity, Wext. However, the reduction of the step frequency leads to a decrease of the power to accelerate the limbs relatively to the centre of gravity, Wint, and, possibly, of the total power Wtot = Wext + Wint. 2. In this study we measured Wext using a force platform, Wint by motion picture analysis, and calculated Wtot during human running at six given speeds (from 5 to 21 km h-1) maintained with different step frequencies dictated by a metronome. The power was calculated by dividing the positive work done at each step by the duration of the step (step-average power) and by the duration of the positive work phase (push-average power). 3. Also in running, as in walking, a change of the step frequency at a given speed has opposite effects on Wext, which decreases with increasing step frequency, and Wint, which increases with frequency; in addition, a step frequency exists at which Wtot reaches a minimum. However, the frequency for a minimum of Wtot decreases with speed in running, whereas it increases with speed in walking. This is true for both the step-average and the push-average powers. 4. The frequency minimizing the step-average power equals the freely chosen step frequency at about 13 km h-1: it is higher at lower speeds and lower at higher speeds. The frequency minimizing the push-average power approaches the freely chosen step frequency at high speeds (around 22 km h-1 for our subjects). 5. It is concluded that the increase of the vertical push does reduce the step-average power, but that a limit is set by the increase of the push-average power. Between 13 and 22 km h-1 the freely chosen step frequency is intermediate between a frequency minimizing the step-average power, eventually limited by the maximum oxygen intake (aerobic power), and a frequency minimizing the push-average power, set free by the muscle immediately during contraction (anaerobic power). The first need prevails at the lower speed, the second at the higher speed.