For a classical particle undergoing nonlinear interaction with a wave in dielectric medium, a perturbation theory is developed, showing that the particle motion can be described in terms of an effective parallel mass which can become negative. A relativistic particle interacting with a circularly polarized wave and a static magnetic field is studied as an example. For the three stationary orbits corresponding to the same velocity parallel to the magnetic field, the conditions are found under which all these equilibria are centerlike, or neutrally stable. It is shown that a negative parallel mass is realized in the vicinity of the intermediate-energy equilibrium and can lead to a plasma collective instability.