Natural enemies such as predators and parasites are known to shape intra-specific variability of behaviour and personality in natural populations, yet several key questions remain: (1) What is the relative importance of predation versus parasitism in shaping intra-specific variation of behaviour across generations? (2) What are the contributions of genetic and plastic effects to this behavioural divergence? And (3) to what extent are responses to predation and parasitism repeatable across independent evolutionary lineages? We addressed these questions using Trinidadian guppies (Poecilia reticulata) (1) varying in their exposure to dangerous fish predators and Gyrodactylus ectoparasites, for (2) both wild-caught F0 and laboratory-reared F2 individuals and coming from (3) multiple independent evolutionary lineages (i.e. independent drainages). Several key findings emerged. First, a population's history of predation and parasitism influenced behavioural profiles, but to different extent depending on the behaviour considered (activity, shoaling or boldness). Second, we had evidence for some genetic effects of predation regime on behaviour, with differences in activity of F2 laboratory-reared individuals, but not for parasitism, which had only plastic effects on the boldness of wild-caught F0 individuals. Third, the two lineages showed a mixture of parallel and non-parallel responses to predation/parasitism, with parallel responses being stronger for predation than for parasitism and for activity and boldness than for shoaling. These findings suggest that different sets of behaviours provide different pay-offs in alternative predation/parasitism environments, and that parasitism have more transient effects in shaping intra-specific variation of behaviour than does predation.