Endogenous cycles cannot emerge in one-sector monetary overlapping generations models when there is intertemporal substitutability, even if returns to scale are increasing. In this article, we show that the conclusions are different when there are two sectors. Considering a two-sector monetary overlapping generations economy, we assume that in each sector, households consume the two goods produced in the economy and firms produce one final good under an internal constant returns to scale technology. However, returns to scale are increasing at the social level because there are sector specific externalities. In this framework, we show that endogenous cycles can occur when households prefer to consume the good produced in the other sector. This result is essentially due to the fact that aggregate consumption in each sector highly depends on the price of the good produced in the other sector. Moreover, we can notice that it does not depend on the substitutability or complementarity between the two goods.