We propose the Gaussian-Linear Hidden Markov model (GLHMM), a generalisation of different types of HMMs commonly used in neuroscience. In short, the GLHMM is a general framework where linear regression is used to flexibly parameterise the Gaussian state distribution, thereby accommodating a wide range of uses—including unsupervised, encoding, and decoding models. GLHMM is available as a Python toolbox with an emphasis on statistical testing and out-of-sample prediction—that is, aimed at finding and characterising brain–behaviour associations. The toolbox uses a stochastic variational inference approach, enabling it to handle large data sets at reasonable computational time. The GLHMM can work with various types of data, including animal recordings or non-brain data, and is suitable for a broad range of experimental paradigms. For demonstration, we show examples with fMRI, local field potential, electrocorticography, magnetoencephalography, and pupillometry.