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Ensemble approaches are commonly used techniques to improving a system by combining multiple model predictions. Additionally these schemes allow the uncertainty, as well as the source of the uncertainty, to be derived for the prediction. Unfortunately these benefits come at a computational and memory cost. To address this problem ensemble distillation (EnD) and more recently ensemble distribution distillation (EnDD) have been proposed that compress the ensemble into a single model, representing either the ensemble average prediction or prediction distribution respectively. This paper examines the application of both these distillation approaches to a sequence prediction task, grammatical error correction (GEC). This is an important application area for language learning tasks as it can yield highly useful feedback to the learner. It is, however, more challenging than the standard tasks investigated for distillation as the prediction of any grammatical correction to a word will be highly dependent on both the input sequence and the generated output history for the word. The performance of both EnD and EnDD are evaluated on both publicly available GEC tasks as well as a spoken language task.