The nonlinear propagation of an arbitrarily polarized electromagnetic wave in a uniform plasma is studied. It is shown that nonlinear effects cause precession of the polarization ellipse as the wave propagates. The ellipticity remains constant, but the orientation of the principal axes is rotated relative to its initial value. A relativistic Vlasov model is used to study nonlinear frequency shifts as well as self‐precession, in a plasma of arbitrary temperature. Even whenT3 ≫ mec2, the qualitative nature of these two processes remains unchanged, although their dependence on the plasma density is altered in significant ways. Implications of these effects for plasma instabilities driven by strong electromagnetic waves are briefly discussed.