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Continual learning has recently attracted attention from the research community, as it aims to solve long-standing limitations of classic supervisedly-trained models. However, most research on this subject has tackled continual learning in simple image classification scenarios. In this paper, we present a benchmark of state-of-the-art continual learning methods on video action recognition. Besides the increased complexity due to the temporal dimension, the video setting imposes stronger requirements on computing resources for top-performing rehearsal methods. To counteract the increased memory requirements, we present two method-agnostic variants for rehearsal methods, exploiting measures of either model confidence or data information to select memorable samples. Our experiments show that, as expected from the literature, rehearsal methods outperform other approaches; moreover, the proposed memory-efficient variants are shown to be effective at retaining a certain level of performance with a smaller buffer size.