We investigate how imperfect competition affects the occurrence and the properties of endogenous, rational expectations business cycles in an overlapping generations model with constant returns to scale in production. The model has explicit product and labor markets all characterized by monopolistic competition. An implicit assumption of barriers to entry justifies that the number of firms is fixed even when positive profits occur. It turns out that both market power of firms on the product markets and market power of unions on the labor markets make the occurrence of cycles more likely. In particular, imperfect competition on the product markets and the positive profits associated with it may have the effect that there is a cycle even if the labor supply curve is increasing in the real-wage rate. For competitive cycles is required not only a decreasing labor supply curve, but a wage elasticity below -½ (at stationary equilibrium). Market power on the labor markets may have the effect that imperfectly competitive cycles are in accordance with certain empirical regularities (some well known, some reported in the paper) concerning fluctuations in output and involuntary unemployment. Since involuntary unemployment does not occur under perfect competition such regularities are incompatible with competitive cycles