We derive an analytical solution for the Josephson plasma resonance of
superconducting multilayers. This analytical solution is derived main
ly for low-T-c systems with magnetic coupling between the superconduct
ing layers. but many features of our results are more general, and thu
s an application to the recently derived plasma resonance phenomena fo
r high-T-c superconductors of the Bi2Sr2CaCu2Ox type is discussed. Our
approach allows us to give full details of the different plasma reson
ance excitations, and we also predict the existence of new nonlinear e
ffects, so far only identified in single junctions.