A study is made into the occurrence of shimmy oscillations in a dual-wheel main landing gear. Nonlinear equations of motion are developed for the system, and various effects are considered, including gyroscopic coupling, nonlinear tire properties, geometric nonlinearities, and fluid shock damping. Of particular interest in this study is the presence of freeplay: this is introduced as a lateral play at the apex of the torque link joints. Using bifurcation analysis methods, the dynamics of this system are explored as the forward velocity and loading force acting on the gear are varied. For the zero freeplay case, the system is found to be stable over its physical operating range with shimmy oscillations appearing only for extreme loading forces and speed. However, with the introduction of freeplay, shimmy may be observed over more typical operating conditions, and the resulting oscillations are found to scale linearly with freeplay magnitude. The parameter plane of forward velocity and loading force is then further subdivided into areas of different types of dynamics. With the inclusion of freeplay one observes the appearance of low-frequency and high-frequency shimmy oscillations, bistable behavior, and stationary solutions of nonzero yaw. Considering the desirable case in which no shimmy occurs, the set of allowable freeplay profiles that satisfy a conservative stability criteria is defined.