The energetics of leaping (porpoising) in aquatic animals is investigated employing two simple hydromechanical models. The first compares the energy required for swimming at different depths below the surface with that for leaping, the second is employed to calculate maximum cruising speeds in fish and cetaceans for the cases of laminar and turbulent boundary layer flow. Leaping is energetically less efficient than swimming close to the surface up to a certain speed (crossover speed) after which it is more efficient. It is shown that dolphins ought to be capable of reaching the required crossover speeds even if subject to a turbulent boundary layer. This is not so for the larger cetaceans that have been observed to porpoise (e.g. killer whales, Orcinus orca). However, crossover speeds for leaping are well within their scope for the case of a boundary layer that is half laminar and half turbulent. Crossover speeds in pelagic animals that do not undulate a substantial proportion of their body in swimming (e.g. baleen whales and penguins) are relatively high. The crossover speeds of the baleen whales are about four times their observed cruising speeds. It is suggested that these animals swim at speeds at which their filtration apparatus (baleen) operates most efficiently. Pelagic fish do not porpoise and reasons are suggested for this.