We report the results of temporal and spectral analysis performed on the X-
ray pulsar 4U 1538-52 observed by BeppoSAX. We obtained a new estimate of t
he spin period of the neutron star P = 528.24 +/- 0.01 s (corrected for the
orbital motion of the X-ray source): the source is still in the spin-up st
ate, as it has been since 1988. The pulse profile is double peaked, althoug
h significant variations of the relative intensity of the peaks with energy
are present. The broadband (0.12-100 keV) out-of-eclipse spectrum is well
described by an absorbed power law modified by a high-energy cutoff at simi
lar to 16 keV (e-folding energy similar to 10 keV) plus an iron emission li
ne at similar to6.4 keV. A cyclotron line at similar to 21 keV is present.
The width of the line is consistent with thermal Doppler broadening at the
temperature of the exponential cutoff. We searched for the presence of the
second harmonic, previously reported for this source. We found no evidence
of lines at similar to 42 keV, although an absorption feature at 51 keV see
ms to be present (at 99% confidence level). A soft excess, modeled by a bla
ckbody with a temperature of similar to0.08 keV could be present, probably
emitted by the matter at the magnetosphere. We also performed a spectral an
alysis during the X-ray eclipse. The spectral evolution during the eclipse
can be well described by a progressive covering of the primary Comptonizati
on spectrum that is scattered into the line of sight. During the deep eclip
se this spectrum also softens, suggesting that the dust-scattered component
becomes important. An alternative, more complex model, with an emission ir
on line and scattered components (as the one that has been used to fit the
eclipse of Cen X-3), also gives a good fit of the deep-eclipse data.