  Using the ``Scenario Machine'' we have carried out a population synthesis of
X-ray binaries for the purpose of modelling of X-ray luminosity functions
(XLFs) in different types of galaxies: star burst, spiral, and elliptical. This
computer code allows to calculate, by using Monte Carlo simulations, the
evolution of a large ensemble of binary systems, with proper accounting for the
spin evolution of magnetized neutron stars.
  We show that the XLF has no universal type. It depends on the star formation
rate in the galaxy. Also it is of importance to take into account the evolution
of binary systems and life times of X-ray stages in theoretical models of such
functions. We have calculated cumulative and differential XLFs for the galaxy
with the constant star formation rate. Also we have calculated cumulative
luminosity functions for different intervals of time after the star formation
burst in the galaxy and curves depicting the evolution of the X-ray luminosity
after the star formation burst in the galaxy.
