Using a stated preferences survey, the objective of this paper is to investigate the intra- and inter-individual heterogeneity of mode choice, when travel time is subject to variability. By‘inter-individual heterogeneity’ is meant that people are different in terms of attitude to risk and have different utility functions. By ‘intra-individual heterogeneity’ is meant that the behaviour may be different even when performed by the same individual when faced with a different mode of transport. Based on Rank-Dependent Utility Theory, the paper shows that the occurrence of delays associated with train trips is overestimated whereas they are underestimated for car trips. A latent-class logit model offers a somewhat different perspective: if, overall, car users are more likely to perceive possible delays for train trips than for car trips, train users tend to consider the objective occurrence of delays as they are presented in the survey and adopt a risk neutral choice behaviour.