  We present results of the spectral and timing analysis of the X-ray pulsar
LMC X-4 with the NuSTAR observatory in the broad energy range 3-79 keV. Along
with the detailed analysis of the averaged source spectrum, the high-precision
pulse phased-resolved spectra were obtained for the first time. It has been
shown that the comptonization model gives the best approximation of the
obtained spectra. The evolution of its parameters was traced depending on the
pulse phase as well. The search for the possible cyclotron absorption line was
performed for all energy spectra in the 5-55 keV energy range. The obtained
upper limit for the depth of the cyclotron absorption line $\tau\simeq0.15$
($3\sigma$) indicates no cyclotron absorption line in this energy range, which
provides an estimate of the magnitude of the magnetic field on the surface of
the neutron star: $B < 3 \times 10^{11}$ G or $B > 6.5 \times 10^{12}$ G. The
latter one is agree with the estimate of the magnetic field obtained from the
analysis of the power spectrum of the pulsar: $B \sim 3 \times 10^{13}$ G.
Based on results of the pulse phase-resolved spectroscopy we revealed a delay
between maxima of the source emission and the equivalent width of the
fluorescent iron line. This delay can be apparently associated with the travel
time of photons between the emitting regions in the vicinity of the neutron
star and the relatively cold regions where this emission is reflected
(presumably, at the inflowing stream or at the place of an interaction of the
stream and the outer edge of the accretion disk).
