This paper explores the ability of a class of one-sector models to generate endogenous skills cycles. Skills cycles are here defined as endogenous fluctuations of the composition of equilibrium allocation of labor services. We consider a one sector economy in which there exist one type of capital stock and a finite number of different labor services, which are assumed to be heterogeneous along the skill/productivity dimension. We apply the Hopf bifurcation theorem and provide necessary conditions on the model's parameters for having a closed orbit as the economy's stable set. We also develop a numerical example (based on the United States economy) showing how this closed orbit can appear under reasonable parameter values.