There are rich structures in off-task neural activity which are hypothesized to reflect fundamental computations across a broad spectrum of cognitive functions. Here, we develop an analysis toolkit - temporal delayed linear modelling (TDLM) - for analysing such activity. TDLM is a domain-general method for finding neural sequences that respect a pre-specified transition graph. It combines nonlinear classification and linear temporal modelling to test for statistical regularities in sequences of task-related reactivations. TDLM is developed on the non-invasive neuroimaging data and is designed to take care of confounds and maximize sequence detection ability. Notably, as a linear framework, TDLM can be easily extended, without loss of generality, to capture rodent replay in electrophysiology, including in continuous spaces, as well as addressing second-order inference questions, for example, its temporal and spatial varying pattern. We hope TDLM will advance a deeper understanding of neural computation and promote a richer convergence between animal and human neuroscience.