We investigate how imperfect competition affects the occurence and properties of endogenous business cycles with underemployment in an overlapping generations model. We consider a competitive product market in association with an imperfect labour market. The latter is presented in two variants. These differ from each other by the game-theoretical concepts used in the description of market equilibria, namely the cooperative concept of Nash-Bargaining and the noncooperative concept of Nash-Cournot. Although they are different, both cases admit the union-monopoly as a limit case. We show that the existence of cycles depends on the degree of market power. Our results are illustrated for specific preferences and technology.