We propose a method of perturbation analysis of nearly sinusoidal oscillators with shifting bias, obtained by generalizing a method recently discussed in the literature [1] (Buonomo A, Di Bello C. IEEE ΒΉransactions on Circuits and Systems, 1996; CAS-43:953}963). The problem of periodic oscillations is formulated as a regular perturbation problem, P (x)"0, whose peculiarity is that the limiting linear problem, P (x)"0, obtained when the perturbation parameter tends to zero, has a non-purely harmonic solution x "B #A cos . We give a simple condition for the existence of a periodic oscillation and an analytical method for constructing it in the form of a power series in . Unlike the existing perturbation methods, the method here proposed, which remains in the spirit of the bifurcation process of PoincareH , allows us to obtain the coe$cients of the series solution, to an order in as great as we want, using recurrence formulae. The results of the analysis of a typical ΒΈC oscillator are given to show that these formulae are very useful as a practical method for determining all of the characteristics of the periodic oscillation, such as the harmonic content and the frequency correction due to the non-linear e!ect.