  We have used the ESO NTT/EMMI and VLT/FORS1 instruments to examine the LMC
supernova remnant 0540-69.3 as well as its pulsar (PSR B0540-69) and
pulsar-powered nebula in the optical range.Spectroscopic observations of the
remnant covering the range of 3600-7350 A centered on the pulsar produced
results consistent with those of Kirshner et al. (1989), but also revealed many
new emission lines. The most important are [Ne III] 3869, 3967 and Balmer lines
of hydrogen. In both the central part of the remnant, as well as in nearby H II
regions, the [O III] temperature is higher than about 20 000 K, but lower than
previously estimated. For PSR B0540-69, previous optical data are mutually
inconsistent: HST/FOS spectra indicate a significantly higher absolute flux and
steeper spectral index than suggested by early time-resolved groundbased UBVRI
photometry. We show that the HST and VLT spectroscopic data for the pulsar have
more then about 50% nebular contamination, and that this is the reason for the
previous difference. Using HST/WFPC2 archival images obtained in various bands
from the red part of the optical to the NUV range we have performed an accurate
photometric study of the pulsar, and find that the spectral energy distribution
of the pulsar emission has a negative slope with 1.07 +/- 0.2. This is steeper
than derived from previous UBVRI photometry, and also different from the almost
flat spectrum of the Crab pulsar. We also estimate that the proper motion of
the pulsar is 4.9 +/- 2.3 mas/yr, corresponding to a transverse velocity of
1190 +/- 560 km/s, projected along the southern jet of the pulsar nebula.
