In polygynous mating systems, it is often difficult to identify factors contributing to male reproductive success. We sought to determine if particular behavioural, morphological or physiological traits were correlated with male dominance and paternity in a captive population of tammar wallabies (Macropus eugenii), and whether male dominance conferred a reproductive advantage. Four replicate groups were held at a sex ratio of four males to seven females in large outdoor enclosures. A range of behavioural (agonistic and sexual) and morphological (body weight, pes length, testis volume and body condition) measurements were collected and serum testosterone concentrations were determined. Paternity of pouch young was determined using microsatellite loci. This study found that alpha males could be clearly distinguished from lower ranked males based on the frequency of sexual behaviour (mate guarding, checking females and disrupting consorts). Of the five non-behavioural variables, only pes length differed significantly between males of different ranks. Dominance rank was significantly correlated with reproductive success and alpha males that maintained post-copulatory guarding had higher reproductive success than males who did not. Alpha males secured 55% of first copulations and the sire corresponded with the first male to mate with the female 69% of the time. Sires could be clearly distinguished from non-sires based on dominance rank, weight and pes length, and they also tended to be in better condition. These data suggest that the physical size of a male is an important determinant of dominance status and reproductive success, probably by enhancing a male’s competitiveness in combat.