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This paper presents an extension and generalization of the phase-plane method to automatic control systems governed by high-order nonlinear differential equations. A unified procedure of analysis is outlined. It is based on linear transformations in the phase space, correlated with the partial-fraction expansion of transfer functions to separate natural frequencies, and makes use of the root-locus method for the qualitative study of closed-loop stability. The analysis leads to replacing a high-order system with a second-order system which closely approximates the former. Excellent insight is obtained into difficult problems. The method is applied to a study of control systems subject to saturation. Appendix II summarizes the current state of knowledge concerning second-order optimum saturating systems.