The nonlinear dynamics of two magnetic elements with easy-plane magnetic anisotropy and ferromagnetic exchange interaction is considered in the framework of discrete Landau–Lifshitz equations. In the absence of damping, exact solutions of these equations are obtained for the proposed integrable dynamical system. The dynamics of the system, its frequency characteristics, and essentially nonlinear high-amplitude excitations, in particular, with a non-equal distribution of excitation between magnetic elements, have been fully investigated. The results of a theoretical study can be used in the analysis of dynamics of magnetic multilayers excited by a polarized current or a high-frequency field.

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