Faster relearning of an external perturbation, savings, offers a behavioral linkage between motor learning and memory. To explain savings effects in reaching adaptation experiments, recent models suggested the existence of multiple learning components, each shows different learning and forgetting properties that may change following initial learning. Nevertheless, the existence of these components in rhythmic movements with other effectors, such as during locomotor adaptation, has not yet been studied. Here, we study savings in locomotor adaptation in two experiments; in the first, subjects adapted to speed perturbations during walking on a split-belt treadmill, briefly adapted to a counter-perturbation and then readapted. In a second experiment, subjects readapted after a prolonged period of washout of initial adaptation. In both experiments we find clear evidence for increased learning rates (savings) during readaptation. We show that the basic error-based multiple timescales linear state space model is not sufficient to explain savings during locomotor adaptation. Instead, we show that locomotor adaptation leads to changes in learning parameters, so that learning rates are faster during readaptation. Interestingly, we find an intersubject correlation between the slow learning component in initial adaptation and the fast learning component in the readaptation phase, suggesting an underlying mechanism for savings. Together, these findings suggest that savings in locomotion and in reaching may share common computational and neuronal mechanisms; both are driven by the slow learning component and are likely to depend on cortical plasticity. computational motor control; locomotor adaptation; motor learning; split-belt