  We discuss the formation, evolution and observational parameters of the
population of short-period ($<10$ hr) low-mass black-hole binaries (LMBHB).
Their evolution is determined by the orbital angular momentum loss and/or
nuclear evolution of the donors. All observed semidetached LMBHB are observed
as soft X-ray transients (SXTs). The absence of observed short-period stable
luminous X-ray sources with black holes and low-mass optical components
suggests that upon RLOF by the donor, the angular-momentum losses are
substantially reduced. The model with reduced angular-momentum loss reasonably
well reproduces the masses and effective temperatures of the observed
secondaries of SXTs. Theoretical mass-transfer rates in SXTs are consistent
with those deduced from observations only if the accretion discs in LMBHB are
truncated. The population of short-period LMBHB is formed mainly by systems
which at RLOF had unevolved or slightly evolved donors (abundance of hydrogen
in the center $> 0.35$). Our models suggest that a very high efficiency of
common envelopes ejection is necessary to form LMBHB.

Astrophysics