Classical Marr-Albus theories of cerebellar learning employ only cortical sites of plasticity. However, tests of these theories using adaptive calibration of the vestibulo-ocular reflex (VOR) have indicated plasticity in both cerebellar cortex and the brainstem. To resolve this long-standing conflict, we attempted to identify the computational role of the brainstem site, by using an adaptive filter version of the cerebellar microcircuit to model VOR calibration for changes in the oculomotor plant. With only cortical plasticity, introducing a realistic delay in the retinal-slip error signal of 100 ms prevented learning at frequencies higher than 2.5 Hz, although the VOR itself is accurate up to at least 25 Hz. However, the introduction of an additional brainstem site of plasticity, driven by the correlation between cerebellar and vestibular inputs, overcame the 2.5 Hz limitation and allowed learning of accurate high-frequency gains. This cortex-first learning mechanism is consistent with a wide variety of evidence concerning the role of the flocculus in VOR calibration, and complements rather than replaces the previously proposed brainstem-first mechanism that operates when ocular tracking mechanisms are effective. These results (i) describe a process whereby information originally learnt in one area of the brain (cerebellar cortex) can be transferred and expressed in another (brainstem), and (ii) indicate for the first time why a brainstem site of plasticity is actually required by Marr-Albus type models when high-frequency gains must be learned in the presence of error delay.