Monogamy is rare among mammals, including marsupials. I studied the social organization of the little-known rock-haunting possum in Kakadu National Park in Northern Australia. Preliminary field observations revealed that the majority of possums live in cohesive groups consisting of a female-male pair and young, suggesting a monogamous mating system. I used radiotracking to determine home range patterns, and observations to measure the degree of symmetry between the sexes in maintaining the pair bond and initiating changes in group activity. I also measured the extent of maternal and paternal indirect and direct care. Nocturnal observations and radiotelemetric data from 3 years showed that six possum groups maintained nonoverlapping home ranges with long-term consorts and young sharing dens. Males contributed more than females to maintaining the pair bond but they contributed equally to parental care. For the first time, the parental behaviours of bridge formation, embracing, marshalling of young, sentinel behaviour and tail beating are reported in a marsupial. Males participated to a high degree in maintaining relationships with one mate and their offspring. Collectively, these results suggest that the mating system of this wild population of rock-haunting possums is obligate social monogamy. Copyright 2000 The Association for the Study of Animal Behaviour.