We tested the hypothesis that sex-biased natal dispersal reduces close inbreeding in American black bears, a solitary species that exhibits nearly complete male dispersal and female philopatry. Using microsatellite DNA and spatial data from reproductively mature bears (≥ 4 years old), we examined the spatial genetic structure of two distinct populations in New Mexico from 1993 to 2000. As predicted, relatedness (r) and the frequency of close relationships (parent–offspring or full siblings) decreased with distance among female dyads, but little change was observed among male or opposite-sex dyads. Neighbouring females were more closely related than neighbouring males. The potential for inbreeding was low. Most opposite-sex pairs that lived sufficiently close to facilitate mating were unrelated, and few were close relatives. We found no evidence that bears actively avoided inbreeding in their selection of mates from this nearby pool, as mean r and relationship frequencies did not differ between potential and actual mating pairs (determined by parentage analysis). These basic patterns were apparent in both study areas despite a nearly two-fold difference in density. However, the sex bias in dispersal was less pronounced in the lower-density area, based on proportions of bears with male and female relatives residing nearby. This result suggests that male bears may respond to reduced competition by decreasing their rate or distance of dispersal. Evidence supports the hypothesis that inbreeding avoidance is achieved by means of male-biased dispersal but also indicates that competition (for mates or resources) modifies dispersal patterns.