We discuss models for calculating the late stages of high-mass binary
evolution. Our discussion is based on evolutionary calculations for in
itial binaries composed of a main-sequence star of mass range 8 to 30
M. with a neutron star companion. The evolution of the primary is foll
owed with the grids of Schaller et al. (1992) until the two stars inte
ract, and simple analytic sts for helium and carbon-oxygen stars. For
non-conservative mass transfer phases, two physical processes are cons
idered: ejection of the excess overflowing matter in the form of jets
from the neutron star and common envelope (CE) evolution. For each mod
el, the code allows us to find the progenitors of the four known doubl
e neutron star systems (NS-NS) in the disk of the Galaxy. We show that
the observed parameters of PSR 1913+16 and PSR 1534+12 are consistent
with one or two stages of mass transfer. In contrast, the wide orbits
of PSR 2303+46 and PSR J1518+49 are the most difficult to reproduce s
ince a moderate orbital shrinkage is required through a CE phase. In p
articular, the likelihood of the formation of PSR J1518+49 appears to
be very sensitive to the adopted formalism for CE-evolution.