  We report on the results of observations of the binary X-ray pulsar LMC X-4
with the Rossi X-ray Timing Explorer. Our analysis of the Doppler delays of the
13.5-s X-ray pulsations yields the most accurate determination of the LMC X-4
orbital parameters available to date. The epoch of orbital phase zero for the
1.4 day orbit is determined with an uncertainty of about 20 s, and is combined
with 5 earlier determinations of the epoch of phase zero to obtain the first
high significance measurement of the rate of change in the orbital period. We
find that the orbital decay timescale is close to 1,000,000 years.
  We present data on one of three strong X-ray flares as well as
energy-dependent pulse profiles for both non-flaring and flaring time
intervals. The pulse profiles during the non-flaring time intervals are
typically strikingly different from the flare profiles, but at other times can
be similar.
  We reconsider the orbital decay of LMC X-4 in the context of tidal evolution.
We find that, while the orbital decay is most likely driven by tidal
interactions, the asynchronism between the orbit and the rotation of the
companion star is probably maintained by the evolutionary expansion of the
companion star, and that the evidence favors the companion star being in a late
stage of its life on the main sequence.
