  The possibility of radiation of high-energy gamma quanta with energies of the
order of 100 GeV by ultrarelativistic electrons on nuclei in strong X-ray
fields with intensities up to $\sim 10^{27}\ \text{Wcm}^{-2}$ has been
theoretically studied. It is shown that this effect can be realized under
special experimental conditions in the process of resonant spontaneous
bremsstrahlung radiation of ultrarelativistic electrons on nuclei in an
external electromagnetic field. These special experimental conditions determine
the characteristic energy of the electrons. This characteristic energy should
be significantly less than the energy of the initial electrons. Under these
conditions, spontaneous gamma quanta are emitted in a narrow cone with energies
close to the energy of the initial electrons. Moreover, the resonant
differential cross-sections of such processes can exceed the corresponding
differential cross-section without an external field by twenty orders of
magnitude. The results obtained can explain the occurrence of high-energy gamma
quanta near pulsars and magnetars.
