  We present results of the analysis of super-Eddington flares registered from
the X-ray pulsar LMC X-4 by the NuSTAR observatory in the broad energy range
3-79 keV. The pulsar spectrum is well described by the thermal comptonization
model both in a quiescent state and during flares, when the peak luminosity
reaches values $L_{\rm x} \sim (2-4)\times10^{39}$ erg s$^{-1}$. An important
feature, found for the first time, is that the order of magnitude increase in
the luminosity during flares is observed primarily at energies below 25-30 keV,
whereas at higher energies (30-70 keV) the shape of the spectrum and the source
flux remain practically unchanged. The luminosity increase is accompanied by
changes in the source pulse profile -- in the energy range of 3-40 keV it
becomes approximately triangular, and the pulsed fraction increases with
increasing energy, reaching 60-70% in the energy range of 25-40 keV. The paper
discusses possible changes in the geometry of the accretion column, which can
explain variations in spectra and pulse profiles.
