  We study the formation of low-mass X-ray binaries with a black hole as
accreting object. The performed semi-analytic analysis reveals that the
formation rate of black holes in low-mass X-ray binaries is about two orders of
magnitude smaller than that of systems with a neutron star as accretor. This is
contradicted by the six observed systems, which are all transients, which
suggest that the majority of these systems has not been seen jet. The birthrate
for both type of objects are expected to be similar (for reviews see Cowley
1992, Tanaka & Lewin 1995). Solution of this conundrum requires either that
stars with masses less than 20~\msun can evolve into black holes, or that
stellar wind from a member of a binary is accompanied by a much larger loss of
angular momentum than hitherto assumed.
