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Biomechanical studies of human walking reveal that compliance plays an important role at least in natural and smooth motions as well as for self-stabilization. Inspired by this, we present here the development of a new lower leg segment of the dynamic biped robot "RunBot". This new lower leg segment features a compliant ankle connected to a flat foot. It is mainly employed to realize robust self-stabilization in a passive manner. In general, such self-stabilization is achieved through mechanical feedback due to elasticity. Using real-time walking experiments, this study shows that the new lower leg segment improves dynamic walking behavior of the robot in two main respects compared to an old lower leg segment consisting of rigid ankle and curved foot: 1) it provides better self-stabilization after stumbling and 2) it increases passive dynamics during some stages of the gait cycle of the robot; i.e., when the whole robot moves unactuated. As a consequence, a combination of compliance (i.e., the new lower leg segment) and active components (i.e., actuated hip and knee joints) driven by a neural mechanism (i.e., reflexive neural control) enables RunBot to perform robust self stabilization and at the same time natural, smooth, and energy efficient walking behavior without high control effort.