Processing motor errors is essential for online control of goal-directed movements and motor learning. Evidence from psychophysical and imaging studies supports the long-standing view that error processing is central to cerebellar function. The dominant view is that error-related signals are encoded in the complex spike discharge of Purkinje cells. However, the findings are inconsistent on whether complex spike activity correlates with motor errors. Recently, we examined if simple spike firing carries error signals in monkeys trained to manually track a randomly moving target. The task requires continuous processing of motor errors characterized by the relative movements between the hand-driven cursor and the target center. Linear regression models show that error parameters are robustly represented in the simple spike activity of most Purkinje cells. At the single cell level, the error signals are encoded independently and integrated with kinematic signals. In a large majority of Purkinje cells, correlation strengths between the simple spike discharge and an error parameter have bimodal profiles with respect to time, exhibiting a local maxima corresponding to firing leading the behavior and another one corresponding to firing lagging behavior. The bimodal temporal profiles suggest that individual error parameters are dually encoded as both an internal prediction used for feedback-independent, compensatory movements and the actual sensory feedback used to monitor performance. Approximately 75 % of the dual representations have opposing modulations of the simple spike activity, one increasing firing and the other depressing firing, as reflected by the reversed signs of the regression coefficients corresponding to the local maxima of the R (2) profile. These dual representations of individual parameters with opposing modulation of the simple spike firing are consistent with the signals needed to generate sensory prediction errors used to update an internal model.