Aquaculture producers' desire animals that are better able to tolerate and survive stress, but selecting animals with these traits is hampered by a lack of reliable stress indicators in aquatic organisms. Here we undertake a preliminary study to explore behavioural response, in terms of distance travelled, under differing stress histories, in greenlip abalone Haliotis laevigata. Movement trials were performed on labelled abalone of known pedigree relationships by measuring distance and direction travelled in a grid marked slab tank with unidirectional current. Animal and sire models were fitted to the data using a Markov chain Monte Carlo multi trait generalised linear mixed effect model. Distance travelled with respect to water flow was found to be influenced by stress inflicted by sampling tentacles either immediately prior to the movement trial, or inflicted > 24. hours prior to the trial (P<0.05), while distance travelled from the starting grid (not direction) was significantly affected by stress inflicted > 24. hours prior to the movement trials (P<0.05), which may be indicative of a delayed or accumulated stress response. There was no evidence that abalone size (length or weight), or the accumulated effects of handling, influenced the distance travelled or direction. The narrow sense heritability of distance and direction travelled was low (0.05 and 0.07 respectively), but significantly greater than zero (95% Bayesian confidence intervals of 0.02-0.16 and 0.03-0.18 respectively), while that of weight and length were moderate to high (>0.4). Parental origin affected distance travelled, such that progeny with parents whose ancestors were selected for faster growth rate for 3 generations, moved longer distances. This difference between animals with different parental origins was exacerbated by stress. The results suggest that behaviour could be a good indicator of some forms of stress.