Humans are capable of learning numerous motor skills, but newly acquired skills may be abolished by subsequent learning. Here we ask what factors determine whether interference occurs in motor learning. We speculated that interference requires competing processes of synaptic plasticity in overlapping circuits and predicted specificity. To test this, subjects learned a ballistic motor task. Interference was observed following subsequent learning of an accuracy-tracking task, but only if the competing task involved the same muscles and movement direction. Interference was not observed from a non-learning task suggesting that interference requires competing learning. Subsequent learning of the competing task 4 h after initial learning did not cause interference suggesting disruption of early motor memory consolidation as one possible mechanism underlying interference. Repeated transcranial magnetic stimulation (rTMS) of corticospinal motor output at intensities below movement threshold did not cause interference, whereas suprathreshold rTMS evoking motor responses and (re)afferent activation did. Finally, the experiments revealed that suprathreshold repetitive electrical stimulation of the agonist (but not antagonist) peripheral nerve caused interference. The present study is, to our knowledge, the first to demonstrate that peripheral nerve stimulation may cause interference. The finding underscores the importance of sensory feedback as error signals in motor learning. We conclude that interference requires competing plasticity in overlapping circuits. Interference is remarkably specific for circuits involved in a specific movement and it may relate to sensory error signals.