The well-known steady state solution of nonlinear oscillatory circuits based on the use of Fourier series, the so-called harmonic balance, is a powerful method because of its wide applicability. Yet, this method has not only difficulties to solve transcendental equations or algebraic equations of higher orders, but gives no transient state solution. The harmonic approximation and the extended harmonic approximation defined in this report are linearization methods which give approximations of steady state and transient state simultaneously. Furthermore the method enables an unification and extension of miscellaneous linearization methods.