Abstract:The nonlinear problems are frequently found in practical engineering. Among the common methods applied for these problems are the multiple scale method, the integral calculus method, the average method, and the homotopy method, but they have very limited capability in real applications. The nonlinear oscillations of the Duffing equations are studied by means of the method of linearization and correction, and the approximate solutions are compared with the exact solutions. With Maple 9.0, the curves of the period, the absolute error and the relative error are plotted against the parameter . It is concluded that the period decreases and the relative error increases with the increase of parameter ; as compared to the exact solution, the approximate solution is simple, with high accuracy and lower relative error. So the method of linearization and correction is very useful in solving problems of nonlinear oscillations.