Learning from motor errors that occur across different limbs is essential for effective tool use, sports training, and rehabilitation. To probe the neural organization of error-driven learning across limbs, we asked whether learning opposing visuomotor mappings with the two arms would interfere. Young right-handers first adapted to opposite visuomotor rotations A and B with different arms and were then reexposed to A 24 h later. We observed that relearning of A was never faster nor were initial errors smaller than prior A learning, which would be expected if there was no interference from B. Rather, errors were greater than or similar to, and learning rate was slower than or comparable to, previous A learning depending on the order in which the arms learned. This indicated robust interference between the motor memories of A and B when they were learned with different arms in close succession. We then proceeded to uncover that the order-dependent asymmetry in performance upon reexposure resulted from asymmetric transfer of learning from the left arm to the right but not vice versa and that the observed interference was retrograde in nature. Such retrograde interference likely occurs because the two arms require the same neural resources for learning, a suggestion consistent with that of our past work showing impaired learning following left inferior parietal damage regardless of the arm used. These results thus point to a common neural basis for formation of new motor memories with different limbs and hold significant implications for how newly formed motor memories interact. NEW & NOTEWORTHY In a series of experiments, we demonstrate robust retrograde interference between competing motor memories developed through error-based learning with different arms. These results provide evidence for shared neural resources for the acquisition of motor memories across different limbs and also suggest that practice with two effectors in close succession may not be a sound approach in either sports or rehabilitation. Such training may not allow newly acquired motor memories to be stabilized. © 2018 American Physiological Society. All rights reserved.