Collective modes in a relativistic meson-nucleon system are investigated. The baryon ground state is treated in a mean-field approximation while the meson propagators are described with a relativistic random-phase approximation. Three types of collective modes are found: zero-sound, meson-branch modes, and modes which indicate an instability of the mean-field theory ground state. The mixing of scalar and vector mesons prevents the propagation of zero-sound at saturation density. This is in sharp contrast to nonrelativistic models which often have zero-sound. There is also important mixing between meson and nucleon-antinucleon excitations which greatly effect meson branch modes.