Modal coupling in the dynamics of a cantilever beam attached to a rotating body is investigated using a coupled, non-linear three-degree-of-freedom model which includes the effects of centrifugal stiffening. The near-resonant response of two lateral modes (one in-plane and one out-of-plane as defined by the plane of rotation) driven by a peridoic out-of-plane excitation is examined for the case in which the natural frequencies of the lateral modes are commensurate in a near one-to-one ratio. The existence and stability of periodic solutions are examined using a second order perturbation analysis. Regions in the system parameter space are identified where single- or multi-mode response may occur. Typical responses involve Hopf, saddle node and pitchfork bifurcations.