  We investigate the star formation history of the central regions of four
Luminous Compact Blue Galaxies (LCBGs). LCBGs are blue (B-V<0.6), compact
(MU_B<21.5 mag arcsec^-2) galaxies with absolute magnitudes M_B brighter than
-17.5. The LCBGs analyzed here are located at 0.436<z<0.525. They are among the
most luminous (M_B < -20.5), blue (B-V < 0.4) and high surface brightness (MU_B
< 19.0 mag arcsec^-2) of this population. The observational data used were
obtained with the HST/STIS spectrograph, the HST/WF/PC-2 camera and the
HST/NICMOS first camera. We find evidence for multiple stellar populations. One
of them is identified as the ionizing population, and the other one corresponds
to the underlying stellar generation.
  The estimated masses of the inferred populations are compatible with the
dynamical masses, which are typically 2--10x 10^9 M_sun. Our models also
indicate that the first episodes of star formation the presented LCBGs
underwent happened between 5 and 7 Gyr ago.
  We compare the stellar populations found in LCBGs with the stellar
populations present in bright, local HII galaxies, nearby spheroidal systems
and Blue Compact Dwarf Galaxies. It turns out that the underlying stellar
populations of LCBGs are similar yet bluer to those of local HII galaxies. It
is also the case that the passive color evolution of the LCBGs could convert
them into local Spheroidal galaxies if no further episode of star formation
takes place. Our results help to impose constraints on evolutionary scenarios
for the population of LCBGs found commonly at intermediate redshifts.
