A perturbation analysis of nonlinear wheel shimmy in aircraft landing gear is presented for nonlinear models that include terms due to coulomb friction between the oleo struts and freeplay in the torque links. The method of multiple timescales is used to obtain general expressions for the limit-cycle amplitude and the frequency that are functions of ground speed. The analysis shows that stable or unstable limit cycles can exist for taxi speeds above or below a critical value with stability of the limit cycles being determined by the sign of a computed coefficient. When only coulomb friction is present, an unstable limit cycle exists. When only freeplay is present, a stable limit cycle exists. When both coulomb friction and freeplay are present, it is shown that stable and unstable limit cycles and a turning point can exist depending on the system parameter values. The solution method is applied to a simple shimmy model, and results from the perturbation analysis are shown to be in good agreement with those obtained by direct numerical integration of the nonlinear shimmy equations.