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Simple locomotion algorithms provide balance for machines that run on one leg. The generalization of these one-leg algorithms for control of machines with several legs is explored. The generalization is quite simple when muitilegged systems run with gaits that use the support legs one at a time. For these gaits the one-leg algorithms can be used to control multilegged running. The concept of a virtual leg is introduced to further extend the approach to gaits that use the legs in pairs, such as the trot, the pace, and the bound. These quadruped running gaits map into gaits that use one virtual leg for support at a time, for which the one-leg algorithms can provide control. This approach was used in laboratory experiments to control a quadruped machine that runs with a trotting gait.