The dispersion relation of the nonlocal plasmon spectrum of a layered two-dimensional electron gas (2DEG) at low temperature in a quantizing magnetic field perpendicular to the layers is examined. Magnetoplasmons of this system have been studied by others, but they have considered only the lowest band in the plasmon spectrum. The excitation spectrum of a 2DEG has been found to have branches analogous to “Bernstein” modes near multiples of the cyclotron frequency for n≥2. For a periodic array of 2DEG layers, the Bernstein modes interact to form bands. Explicit results are presented for the degenerate case in the high-field quantum limit, when all electrons are in the lowest Landau eigenstate.