  As has only recently been recognized, X-ray binaries with intermediate-mass
secondaries are much more important than previously believed. To assess the
relative importance of low- and intermediate-mass X-ray binaries (LMXBs and
IMXBs), we have initiated a systematic study of these systems consisting of two
parts: an exploration of the evolution of LMXBs and IMXBs for a wide range of
initial masses and orbital periods using detailed binary stellar evolution
calculations, and an integration of these results into a Monte-Carlo binary
population synthesis code. Here we present some of the main results of our
binary calculations and some preliminary results of the population synthesis
study for a ``standard'' reference model. While the inclusion of IMXBs improves
the agreement with the observed properties of ``LMXBs'', several significant
discrepancies remain, which suggests that additional physical processes need to
be included in the model.
