Transfers and services are frequent in the animal kingdom. However, there is no clear evidence in animals that such transactions are based on weighing costs and benefits when giving or returning favours and keeping track of them over time (i.e. calculated reciprocity). We tested two orang-utans (Pongo pygmaeus abelii) in a token-exchange paradigm, in which each individual could exchange a token for food with the experimenter but only after first obtaining the token from the other orang-utan. Each orang-utan possessed tokens valuable to their partner but useless to themselves. Both orang-utans actively transferred numerous tokens (mostly partner-valuable) to their partner. One of the orang-utans routinely used gestures to request tokens while the other complied with such requests. Although initially the transfers were biased in one direction, they became more balanced towards the end of the study. Indeed, data on the last three series produced evidence of reciprocity both between and within trials. We observed an increase in the number and complexity of exchanges and alternations. This study is the first experimental demonstration of the occurrence of direct transfers of goods based on calculated reciprocity in non-human-primates.