  We show that black-hole High-Mass X-ray Binaries (HMXBs) with O- or B-type
donor stars and relatively short orbital periods, of order one week to several
months may survive spiral in, to then form Wolf-Rayet (WR) X-ray binaries with
orbital periods of order a day to a few days; while in systems where the
compact star is a neutron star, HMXBs with these orbital periods never survive
spiral-in. We therefore predict that WR X-ray binaries can only harbor black
holes. The reason why black-hole HMXBs with these orbital periods may survive
spiral in is: the combination of a radiative envelope of the donor star, and a
high mass of the compact star. In this case, when the donor begins to overflow
its Roche lobe, the systems are able to spiral in slowly with stable Roche-lobe
overflow, as is shown by the system SS433. In this case the transferred mass is
ejected from the vicinity of the compact star (so-called "isotropic
re-emission" mass loss mode, or "SS433-like mass loss"), leading to gradual
spiral-in. If the mass ratio of donor and black hole is $>3.5$, these systems
will go into CE evolution and are less likely to survive. If they survive, they
produce WR X-ray binaries with orbital periods of a few hours to one day.
  Several of the well-known WR+O binaries in our Galaxy and the Magellanic
Clouds, with orbital periods in the range between a week and several months,
are expected to evolve into close WR-Black-Hole binaries,which may later
produce close double black holes. The galactic formation rate of double black
holes resulting from such systems is still uncertain, as it depends on several
poorly known factors in this evolutionary picture. It might possibly be as high
as $\sim 10^{-5}$ per year.
