  A theory of the nonlinear plasma waves in graphene is developed in the
nonperturbative regime. The influence of strong electric fields on the position
and linewidth of plasma resonances in the far-infrared transmission
experiments, as well as on the wavelength and the propagation length in the
scanning near-field optical microscopy experiments is studied. The theory shows
that the fields of order of a few to a few tens of kV/cm should lead to a red
shift and broadening of plasma resonances in the first type and to a reduction
of the wavelength and the propagation length in the second type of experiments.
