  The possibilities of observing some nonlinear electrodynamic effects, which
can be manifested in hard emission of X-ray, gamma ray pulsars and magnetars by
X-ray and gamma ray astronomy methods are discussed. The angular resolution and
sensitivity of modern space observatories give the opportunity to study the
nonlinear electrodynamic effects, which can occur in very strong magnetic
fields of pulsars ($B\sim 10^{12}$ G) and magnetars ($B\sim 10^{15}$ G). Such
magnetic field magnitudes are comparable with the typical value of magnetic
field induction necessary for manifestation of electrodynamics non-linearity in
vacuum. Thus, near a magneticneutron star the electromagnetic emission should
undergo nonlinear electrodynamic effects in strong magnetic fields (such as
bending of rays, fluxes dispersing, changing of spectra and polarization
states). Manifestations of these effects in detected hard emission from
magnetic neutron stars are discussed on the base of nonlinear generalizations
of the Maxwell equation in vacuum. The dispersion equations for electromagnetic
waves propagating in the magnetic dipole field were obtained in the framework
of these theories.The possibility of observing the bending of a ray and gamma
ray flux dispersing in the neutron star magnetic field are analyzed. The only
nonlinear electrodynamicseffect, which can be measured principally, is the
effect of gamma ray flux dispersion by the neutron star magnetic field.
Studying this effect we can also obtain information on the nonlinear
electrodynamics bending of a ray in the source. The main qualitative difference
in predictions of different nonlinear electrodynamics theories are discussed.
