One of the central interests of animal movement ecology is relating movement characteristics to behavioural characteristics. The traditional discrete-time statistical tool for inferring unobserved behaviours from movement data is the hidden Markov model (HMM). While the HMM is an important and powerful tool, sometimes it is not flexible enough to appropriately fit the data. Data for marine animals often exhibit conditional autocorrelation, self-dependence of the step length process that cannot be explained solely by the behavioural state, which violates one of the main assumptions of the HMM. Using a grey seal track as an example we motivate and develop the conditionally autoregressive hidden Markov model (CarHMM), a generalization of the HMM designed specifically to handle conditional autocorrelation. In addition to introducing and examining the new CarHMM with numerous simulation studies, we provide guidelines for all stages of an analysis using either an HMM or CarHMM. These include guidelines for pre-processing location data to obtain deflection angles and step lengths, model selection, and model checking. In addition to these practical guidelines, we link estimated model parameters to biologically relevant quantities such as activity budget and residency time. We also provide interpretations of traditional “foraging” and “transiting” behaviours in the context of the new CarHMM parameters.