Golden-rumped elephant-shrews Rhynchocyon chrysopygus are primarily monogamous, males and females defending joint territories for long periods and probably for life. However, males may occasionally solicit extra-pair copulations from neighbouring females and annex their territories if the resident male disappears for any reason. Males provide no direct paternal care, and the adaptive significance of monogamy in this species is unclear. Although it is possible that males provide some indirect benefits to the female and her offspring, these are unlikely to be substantial. Males and females spend little time together, so males are unlikely to provide additional protection from predators, and there is no evidence that the presence of a territorial male reduces the costs of territorial defence for the female. Females were able to breed successfully when mated bigamously, demonstrating that the undivided assistance of the male is not essential for successful rearing of offspring. The fact that male elephant-shrews occasionally attempt to defend more than one female suggests that polygyny would be beneficial for males. However, defending two territories is costly, resulting in increased activity and weight loss, and higher rates of intrusion by neighbouring males. Female elephant-shrews do not occupy particularly large home ranges for their body size. The results suggest that the high costs of defending a territory large enough to encompass the ranges of more than one female, combined with the greater probability of being cuckolded, make defending more than one female a poor option for male elephant-shrews.