Many cooperatively breeding animals actively defend a territory containing resources such as food and shelter, which are essential for reproduction. Some observations, however, indicate that conflicts between groups are often triggered by the attempts of males or females, or both, to gain extra-group copulations. We studied interactions between 12 groups of banded mongooses (Mungos mungo) in Uganda to test whether the frequency of inter-group encounters was linked to the reproductive status of females, and conducted an experiment to examine the responses of individuals to mongooses from other groups. The rate at which focal groups fought with other groups was higher when its females were in estrous, suggesting that many fights take place over access to mates. Both males and estrous females were instrumental in instigating encounters with rival groups, and extra-group copulation in the midst of a fight was observed on three occasions. We experimentally simulated encounters with foreign individuals by presenting each of six groups with cages containing a male and a female from a rival group. Subordinate males were the first to investigate these 'intruders', spent more time around the intruders' cages, and were more aggressive to the intruders than either dominant males or females. Subordinate males directed more attention and aggression towards the male intruder than the female intruder. We suggest that male banded mongooses actively seek extra-group copulations in pursuit of paternity, while females may actively seek extra-group copulations as a way of reducing inbreeding depression.