Correlations between unrelated personality traits in different contexts, often referred to as behavioural syndromes, have been found to exist among individuals. Behavioural syndromes have been documented in a wide variety of taxa and may arise due to correlated behaviours having a similar underlying genetic basis, so that they have become coupled (genetic constraint), or when one hormone acts on several traits (hormonal constraints) or if adaptations to existing selection pressure act simultaneously on multiple traits (adaptive constraints). We examined if there were correlations between boldness and aggression, which would be an indication of a behavioural syndrome in three strains of zebrafish and the guppy. There was some evidence of a boldness and aggression syndrome in only females of two of the zebrafish strains and in the male guppies. Given the limited correlation of these traits within the populations studied, this syndrome was probably due to adaptations to prevailing selection pressures rather than due to genetic constraints.