In this paper, s mathematical model of the nitrogen cycle in aquatic ecosystems is proposed for studying eutrophication in bodies of water. It is presented that for some parameter values all equilibrium states of the system become unstable and a stable limit cycle appears. This is explained by a Hopf bifurcation. The conditions under which the Hopf bifurcation occurs are obtained by the detailed analysis of the model. Some results of numerical computations are also presented.