Cooperation of different generations is crucial to meet many important societal challenges, including climate change or the sustainability of the welfare state. Little is known, however, about different generations’ ability to cooperate in social dilemma situations, and their willingness to enforce social norms of cooperation. We present an experiment with two generations – juniors in their 20ies, and seniors who are 50 years or older, with an average age of 67. They play a repeated prisoner's dilemma (PD) game with third-party punishment. The third party is either a person from the same generation as the players in the PD game or from the other generation, and this is common knowledge. We find that seniors cooperate twice as much as juniors do, irrespective of the generation of the third-party. Moreover, seniors are much stricter as third parties and punish norm violations much more frequently than juniors do. However, the cooperation levels of both generations react hardly to third party punishment, which means that both generations differ strongly in their attempts to enforce norms of cooperation and in their reaction to norm enforcement. These differences across generations may pose a serious threat for the solution of intergenerational problems.