Educational research in cooperative learning suggests that inequity based on perceived status may be an issue with heterogeneous cooperative learning groups. This paper explores issues of status based on race, ethnicity and cultural background in the New Zealand tertiary classroom where there is a diverse mix of domestic and international students. A four-year research project examined attitudes and perceptions of both domestic and international tertiary students towards cooperative learning. The findings of the research project indicate that initial assumptions of relative status and ability of group members have a major effect on the outcomes of the group. These assumptions, demonstrated by both domestic and international students, may be based on expectations of language ability and familiarity with the pedagogical environment, including the assumed norms and behavioural patterns of the host educational setting, and may disadvantage students from different cultural backgrounds. This can become a self-fulfilling prophecy limiting the effective interaction and participation in the group by international students and other students perceived to be of low status, and the development of trust and reciprocal interdependence among group members. Strategies to weaken the effects of status, promote more equitable interaction and foster productive group outcomes are proposed.