A team contest entails both public good characteristics within the teams as well as a contest across teams. In an experimental study, we analyse behaviour in such a team contest when allowing to punish or to reward other team members. Moreover, we compare two types of contest environment: One in which two teams compete for a prize and another one in which we switch off the between-group element of the contest. We find that reward giving, as opposed to punishing, induces higher contributions to the team contest. Furthermore, expenditures on rewarding other co-players are significantly higher than those for punishing.