We propose a novel block for causal video modelling. It relies on a time - space - channel factorisation with dedicated blocks for each dimension: gated linear recurrent units (LRUs) perform information mixing over time, self-attention layers perform mixing over space, and MLPs over channels. The resulting architecture TRecViT is causal and shows strong performance on sparse and dense tasks, trained in supervised or self-supervised regimes, being the first causal video model in the state-space models family. Notably, our model outperforms or is on par with the popular (non-causal) ViViT-L model on large scale video datasets (SSv2, Kinetics400), while having 3x less parameters, 12x smaller memory footprint, and 5x lower FLOPs count than the full self-attention ViViT, with an inference throughput of about 300 frames per second, running comfortably in real-time. When compared with causal transformer-based models (TSM, RViT) and other recurrent models like LSTM, TRecViT obtains state-of-the-art results on the challenging SSv2 dataset. Code and checkpoints are available online \url{https://github.com/google-deepmind/trecvit}.