  We systematically investigate the effects of high supernova kick velocities
on the orbital parameters of post-supernova neutron-star binaries. Using Monte-
Carlo simulations, we determine the post-supernova distributions of orbital
parameters for progeneitors of HMXBs and LMXBs. With the recent distribution of
pulsar birth velocities by Lyne & Lorimer (1994), only about 27% of massive
systems remain bound after the supernova, of which about 26% immediately
experience dynamical mass transfer and possibly merge to become Thorne-Zytkow
objects. The correlations between various orbital parameters can be compared
with observational samples to yield information about supernova kick velocities
and pre-supernova orbital-period distributions. After the supernova, the spins
of most stars in massive systems have large inclinations with respect to their
orbital axes, and a significant fraction of systems (about 20%) contain stars
with retrograde spins. In the case of low-mass companions, we find that about
19% of systems remain bound after the supernova, of which about 57% experience
immediate dynamical mass transfer. There is a tight correlation between the
eccentricity and the post-supernova orbital period in LMXB progeneitors. All
LMXBs with post-supernova periods longer than a few days initially have large
eccentricities (e.g. Cir X-1 is discussed in this context). We use the results
of these calculations to simulate the sky distributions of HMXBs and LMXBs. The
simulated distributions agree with observed samples. Most importantly, the
distribution of Galactic LMXBs is consistent with an ordinary Galactic disk
population which has been widened because of large supernova kicks and does not
require a special population of progenitors.
