In recent years, new theoretical concepts and empirical research greatly increased our understanding concerning the evolution and persistence of cooperative behaviour between unrelated individuals. We now need to complement the evolutionary knowledge with research about the cognitive and the physiological mechanisms underlying cooperative behaviour, and fishes provide suitable study systems. The focus will be on marine cleaning mutualism, where more than 70 species of so called "cleaners" are known to remove ectoparasites but also mucus and scales from so called "clients". We already started to use the diversity of cleaner species for a comparative approach, where we first identify differences between species with respect to dependency on cleaning for their diet, foraging preferences (ectoparasites or mucus), or the probability of repeated interactions with the same clients. We then explore whether differences in these parameters are linked to potential differences in a) how clients reduce mucus feeding by cleaners, b) variation in the cleaners' social cognitive abilities, and c) the effects of endocrine substances on cooperative behaviour. The methods have already largely been developed in studies on the cleaner wrasse Labroides dimidiatus, using partly real clients and partly Plexiglas plates as surrogates. We determine the endocrine modulators of cooperative behaviour in L. dimidiatus, amenable for further testing in the comparative approach. In addition, we study the clients' physiological and immune responses in cleaning interactions. A major new topic will be to determine how variation in the complexity of the natural environment affects the cleaners' decision rules how to treat clients and their cognitive abilities. We have established that differences exist and now have to study their functionality, their ontogeny, and the ecological causes. Apart from cleaning mutualism we also investigate cooperative hunting in fishes. We compare the strategic and cognitive abilities of fish predators with the published evidence on mammalian predators using an experimental approach. The proposed studies are unique with their emphasis on the comparative approach and with the in-depth investigation of the mechanisms underlying cooperative behaviour in non-human animals. The empirical progress will strongly be enhanced through diverse collaborations with theoreticians, aimed at developing both specific game theoretic models and a more general framework on cooperation between unrelated individuals.