Summary: We have described elsewhere an adaptive filter model of cerebellar learning in which the cerebellar microcircuit acts to decorrelate motor commands from their sensory consequences [Dean, Porrill, and Stone, Proceedings of the Royal Society of London, Series B 269 (1503), 1895–1904 (2002)]. Learning stability required the cerebellar microcircuit to be embedded in a recurrent loop, and this has been shown to lead to a simple and modular adaptive control architecture when applied to the linearized 3D vestibular ocular reflex [Porrill, Dean, and Stone, Progress in Brain Research 144, 61–75 (2004)]. Here we investigate the properties of recurrent loop connectivity in the case of redundant and nonlinear motor systems and illustrate them using the example of kinematic control of a simulated two-joint robot arm. We demonstrate that (1) the learning rule does not require unavailable motor error signals or complex neural reference structures to estimate such signals (i.e., it solves the motor error problem) and (2) control of redundant systems is not subject to the nonconvexity problem in which incorrect average motor commands are learned for end-effector positions that can be accessed in more than one arm configuration. These properties suggest a central functional role for the closed cerebellar loops, which have been shown to be ubiquitous in motor systems (e.g., Kelly and Strick, Journal of Neuroscience 23 (23), 8432–8444 (2003).