Frequently changing operating conditions in power systems call for an extensive effort in stability studies. In this paper, a method is developed to determine the constraints due to oscillatory instabilities on the distribution of power generation among the generators of an interconnected system. The method involves calculating the feasibility boundaries in the parameter spaces generated by load references of generating units. These feasibility boundaries correspond to Hopf bifurcations of electromechanical oscillatory modes. In the paper, local and inter-area oscillatory instabilities generated by particular distributions of power generation and loading conditions are demonstrated and discussed.