  We have investigated the temporal variability of the X-ray flux measured from
the high-mass Xray binary LMCX-4 on time scales from several tens of days to
tens of years, i.e., exceeding considerably the orbital period (1.408 days). In
particular, we have investigated the 30-day cycle of modulation of the X-ray
emission from the source (superorbital or precessional variability) and refined
the orbital period and its first derivative. We show that the precession period
in the time interval 1991--2015 is near its equilibrium value $P_{sup} =
30.370$ days, while the observed historical changes in the phase of this
variability can be interpreted in terms of the "red noise" model. We have
obtained an analytical law from which the precession phase can be determined to
within 5\% in the entire time interval under consideration. Using archival data
from several astrophysical observatories, we have found 43 X-ray eclipses in
LMC X-4 that, together with the nine eclipses mentioned previously in the
literature, have allowed the parameters of the model describing the evolution
of the orbital period to be determined. As a result, the rate of change in the
orbital period $\dot P_{orb}/P_{orb}=(1.21\pm0.07)\times10^{-6}$ yr$^{-1}$ has
been shown to be higher than has been expected previously.
