  We report here detailed timing and spectral analysis of two Beppo-SAX
observations of the binary X-ray pulsar LMC X-4 carried out during the low and
high states of its 30.5 days long super-orbital period. Timing analysis clearly
shows 13.5 s X-ray pulsations in the high state of the super-orbital period
which allows us to measure the mid-eclipse time during this observation.
Combining this with two other mid-eclipse times derived earlier with the ASCA,
we derived a new estimate of the orbital period derivative. Pulse-phase
averaged spectroscopy in the high and low states shows that the energy spectrum
in the 0.1 - 10 keV band comprises of a hard power-law, a soft excess, and a
strong iron emission line. The continuum flux is found to decrease by a factor
of ~ 60 in the low state while the decrease in the iron line flux is only by a
factor of ~ 12, suggesting a different site for the production of the line
emission. In the low state, we have not found any significant increase in the
absorption column density. The X-ray emission is found to come from a very
large region, comparable to the size of the companion star. Pulse phase
resolved spectroscopy in the high state shows a pulsating nature of the soft
spectral component with some phase offset compared to the hard X-rays, as is
known in some other binary X-ray pulsars.
