The entrance of new males into non-human primate groups bears high social risk, yet migration is necessary to prevent inbreeding. Males are not always accepted in their new group. In the wild, males may increase the likelihood of successful group entry by choosing a new group based on their own and the group's characteristics. Understanding whether these characteristics also determine a male's ability to enter captive groups is crucial to improve introduction management. This study aims to identify which factors determine male introduction success (i.e. male stays in the group for at least 4 weeks) and long-term stability (i.e. the male does not cause considerable behavioural problems after success) after male introductions in captive groups of rhesus macaques (Macaca mulatta), creating one-male groups. We studied 64 male introductions at the breeding colony of the Biomedical Primate Research Centre in Rijswijk, The Netherlands. 49 (77%) introductions were successful, with the male obtaining a long-term stable social position in the group in 38 (59%) introductions. Introductions of males that reached at least prime age, into groups with more adult females, but without pregnant females were most successful. Moreover, long-term stability was highest when males were heavier, were at least 3.5 years old when they were first removed from their natal group, and groups had few matrilines and no pregnant females were present. Males should be introduced at the time they would naturally immigrate, when they are strongest. Moreover, groups should consist of few large matrilines, as observed in the wild, with philoatric females and males that are removed at natural age. Our study highlights the importance of composing naturalistic groups and mimicking natural migration patterns to maintain long-term stable breeding groups in captivity.