AbstractAn approximate analytical method is developed to estimate the parameter sensitivity of the solution of a set of nonlinear ordinary differential equations describing a system which exhibits periodic behavior. An approximate solution is constructed in terms of both the approximate periodic solution determined from Galerkin equations and the envelope and phase of the oscillation away from such a periodic solution. Parameter sensitivity information is then obtained by examining the parameter variation effect on the approximate solution.Examples of two‐ and three‐dimensional nonlinear systems illustrate this procedure and show that the effect of parameter change on the solution is predicted with sufficient accuracy to make this method useful for nonlinear analysis.