Culturally diverse work groups do not always reach their full potential compared with less diverse groups. As shared values facilitate group functioning, we examined whether constructing shared values among group members is constrained by high degrees of cultural diversity. Following 33 real-life work groups, we investigated how members influenced each other's achievement and relational values over time. Although low and high diversity groups did not differ in initial value similarity between members, they differed in the process of value convergence. In low diversity groups, members developed shared values by influencing each other's values towards consensus. In high diversity groups, however, members did not influence each other's values towards consensus. Low diversity groups also performed better than high diversity groups. These findings extend earlier findings establishing value convergence in culturally homogenous groups and reveal the distinctive processes in highly diverse groups as a focus for interventions to promote diverse group functioning. Copyright © 2014 John Wiley & Sons, Ltd.