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This paper proposes a numerical approximation method for analyzing the steady state and the transient state of sineware oscillator circuits. Since most oscillator circuits contain active and nonlinear elements (e.g., transistors), and inductive capacitive and by-pass components, their circuit equations generally become high-order nonlinear differential equations. The proposed method uses the Newton method to determine the operating point. The variation (ac component) about the operating point is used a variable for establishing a nonlinear differential equation to be solved by means of the Krylov-Bogolyubov-Mitropolsky asymptotic method. The discrete Fourier transform is then applied repeatedly to obtain the second-order approximation for the periodic solutions. The approximation method for transient solutions is also discussed. Finally, an example of a transistorized CR phase-shift oscillator is used to demonstrate the usefulness of the proposed method. The periodic and transient solutions obtained by the proposed method are compared to those of the Runge-Kutta-Gill method. [ABSTRACT FROM AUTHOR]