A condition for the existence of a limit cycle for a class of second-order non-linear control systems with a type zero linear plant is derived. The limit cycle stability is assured whenF(a,b, α, β)/Ecurve has a positive slope at the point of intersection ofF(a,b, α, β) andKloci. A typical second-order non-linear system is analysed for the purpose of illustrating the method of finding the amplitude and frequency of sustained oscillation. The method of studying the effects of variation ofK, α and β on the amplitude and frequency of oscillation of the system is indicated. With regard to this, the proposed method has certain advantages over the usual method of analysis.