To overcome poor signal-to-noise ratios in neuroimaging, data sets are often acquired over repeated trials that form a three-way array of spacetimetrials. As neuroimaging data contain multiple inter-mixed signal components blind signal separation and decomposition methods are frequently invoked for exploratory analysis and as a preprocessing step for signal detection. Most previous component analyses have avoided working directly with the tri-linear structure, but resorted to bi-linear models such as ICA, PCA, and NMF. Multi-linear decomposition can exploit consistency over trials and contrary to bi-linear decomposition render unique representations without additional constraints. However, they can degenerate if data does not comply with the given multi-linear structure, e.g., due to time-delays. Here we extend multi-linear decomposition to account for general temporal modeling within a convolutional representation. We demonstrate how this alleviates degeneracy and helps to extract physiologically plausible components. The resulting convolutive multi-linear decomposition can model realistic trial variability as demonstrated in EEG and fMRI data.