||We investigate models for animal feeding behaviour, with the aim of improving understanding of how animals organise their behaviour in the short term. We consider three classes of model: hidden Markov, latent Gaussian and semi-Markov. Each can predict the typical `clustered' feeding behaviour that is generally observed, however they differ in the extent to which `memory' of previous behaviour is allowed to affect future behaviour. The hidden Markov model has `lack of memory', the current behavioural state being dependent on the previous state only. The latent Gaussian model assumes feeding/non-feeding periods to occur by the thresholding of an underlying continuous variable, thereby incorporating some `short-term memory'. The semi-Markov model, by taking into account the duration of time spent in the previous state, can be said to incorporate `longer-term memory'. We fit each of these models to a dataset of cow feeding behaviour. We find the semi-Markov model (longer-term memory) to have the best fit to the data and the hidden Markov model (lack of memory) the worst. We argue that in view of effects of satiety on short-term feeding behaviour of animal species in general, biologically suitable models should allow `memory' to play a role. We conclude that our findings are equally relevant for the analysis of other types of short-term behaviour that are governed by satiety-like principles.