Genetically determined cerebellar ataxias (CA) are a heterogeneous group of disorders with progressive decline of cerebellar functions. The cerebellum influences internal forward models that play a role in cognitive control, but whether these processes are dysfunctional in CA is unclear. Here, we examined sensory predictive coding processes and response adaptation in CA and healthy controls (HC) using behavioral tests with concomitant EEG recordings. N = 23 patients and N = 29 age- and sex-matched HC were studied. Sensory prediction coding was tested with an auditory distraction paradigm and error-related behavioral adaptation with a visual flanker task. As neurophysiological markers we studied different event-related potentials: the P3a for orientation of attention; the N2 and the error-related negativity (ERN) for cognitive adaptation processes/consequences of response errors; error-related positivity (Pe) for error-awareness; the mismatch negativity (MMN) for sensory predictive coding; and reorientation negativity (RON) for reorientation after unexpected events. Overall reaction times were slower in patients compared to HC, but error rates did not differ. Both in patients and HC, P3a amplitudes were larger in distraction trials, but the P3a amplitude was smaller in patients compared to HC. The MMN as well as behavioral and EEG-correlates of response adaptation (ERN/N2) did not differ between groups, while the Pe was attenuated in patients. During sensory predictive coding, RON amplitudes were significantly larger in HC compared to patients. In HC, but not in patients, RON amplitudes were also larger in deviant compared to frequent trials. Processes generating internal forward models are largely intact in genetically determined CA, whereas updating of mental models and error awareness are disturbed in these patients.