Abstract <p>A basic model is proposed for the mesoscopic dynamics of a magnetically active elastomer (MAE). The MAE unit cell consists of a pair of linearly magnetizable spherical particles embedded in a Kelvin-type viscoelastic elastomer. Forced oscillations of this system under a magnetic field with both constant and variable components are investigated within a specific amplitude–frequency range. In this range, the pair exhibits a distinctive behavior, which consists in a sudden transition from a finite distance between the particles to close contact (collapse). This phenomenon, known as bistability, is described in statics as magnetomechanical hysteresis, where strain as a function of the applied field shows an ambiguous region. It is demonstrated that, depending on the material parameters and field characteristics, various stationary oscillation cycles are possible. In addition, increasing the frequency of the variable field component reduces hysteresis effects. The system behavior at high oscillation frequencies is described qualitatively.</p>