  We present theoretical models for the formation and evolution of populations
of low-mass X-ray binaries (LMXB) in the two elliptical galaxies NGC 3379 and
NGC 4278. The models are calculated with the recently updated StarTrack code
(Belczynski et al., 2006), assuming only a primordial galactic field LMXB
population. StarTrack is an advanced population synthesis code that has been
tested and calibrated using detailed binary star calculations and incorporates
all the important physical processes of binary evolution. The simulations are
targeted to modeling and understanding the origin of the X-ray luminosity
functions (XLF) of point sources in these galaxies. For the first time we
explore the population XLF down to luminosities of 3X10^36 erg/s, as probed by
the most recent observational results (Kim et al., 2006). We consider models
for the formation and evolution of LMXBs in galactic fields with different CE
efficiencies, stellar wind prescriptions, magnetic braking laws and initial
mass functions. We identify models that produce an XLF in excellent agreement
with the observations both in shape and absolute normalization. We also find
that the treatment of the outburst luminosity of transient systems remains a
crucial factor for the determination of the XLF since the modeled populations
are dominated by transient X-ray systems.
