  Intense radiation field can modify plasma properties, the corresponding
refractive index, and lead to such nonlinear propagation effects as
self-focusing. We estimate the corresponding effects in pair plasma, both in
unmagnetized and strongly magnetically dominated case. First, in the
unmagnetized pair plasma the ponderomotive force does not lead to charge
separation, but to density depletion. Second, for astrophysically relevant
plasmas of pulsar magnetospheres, (and possible loci of Fast Radio Bursts),
where cyclotron frequency $\omega_B$ dominates over plasma frequency $\omega_p$
and the frequency of the electromagnetic wave, $\omega_B \gg \omega_p,\,
\omega$, we show that (i) there is virtually no nonlinearity due to changing
effective mass in the field of the wave; (ii) ponderomotive force is $F_p^{(B)}
=- {m_e c^2}/({4 B_0^2}) \nabla E^2$; it is reduced by a factor
$(\omega/\omega_B)^2$ if compared to the unmagnetized case ($B_0$ is the
external magnetic field and $E$ is the electric field of the wave); (iii) for
radiation beam propagating along constant magnetic field in pair plasma with
density $n_\pm$, the ponderomotive force leads to appearance of circular
currents that lead to the decrease of the field within the beam by a factor
$\Delta B/B_0 = 2\pi n_\pm m_e c^2 {E^2}/{B_0^4}$. Applications to the physics
of FRBs are discussed; we conclude that for parameters of FRB's the dominant
magnetic field completely suppresses nonlinear radiation effects.
