Powers higher than the maximal aerobic power can be attained relying on anaerobic lactic and alactic metabolisms as energy source. These metabolisms are analysed separately in this Chapter, where the power and capacity of both have been quantified. Anaerobic lactic metabolism has been treated first, although it is still a controversial issue on quantitative grounds, because several authors denied the possibility of performing a correct estimate of the metabolic energy corresponding to a mole of lactate accumulation in blood. Thus, its analysis is preceded by a preliminary discussion of the principles and assumption behind the concept of energetic meaning of blood lactate accumulation is based. Then, anaerobic alactic metabolism is discussed, for which a distinction between average and instantaneous powers is introduced: the former reflects the rate of ATP resynthesis from the Lohmann's reaction and the latter refers to the maximal rate of ATP hydrolysis and concerns the ATP already available at the contraction site. This analysis shows that the maximal power generated by anaerobic alactic metabolism is extremely high, up to some 20 times higher than the maximal aerobic power for the instantaneous methods. The price to pay for this is an extremely low capacity, so that exercise can be sustained at maximal power only for a very short time, of the order of a few seconds for average power, some milliseconds for instantaneous power. Such an organization of energetic metabolism, with a wide range of powers and capacities for the ensemble of the metabolic pathways, allows animals, humans included, to face the multiple needs that a prey-predator system imposes. In general terms, animals have evolved in such a way that power is highest when capacity is lowest, and vice versa.