  Cygnus X-2 appears to be the descendant of an intermediate-mass X-ray binary
(IMXB). Using Mazzitelli's (1989) stellar code we compute detailed evolutionary
sequences for the system and find that its prehistory is sensitive to stellar
input parameters, in particular the amount of core overshooting during the
main-sequence phase. With standard assumptions for convective overshooting a
case B mass transfer starting with a 3.5 M_sun donor star is the most likely
evolutionary solution for Cygnus X-2. This makes the currently observed state
rather short-lived, of order 3 Myr, and requires a formation rate > 1e-7 - 1e-6
per yr of such systems in the Galaxy. Our calculations show that neutron star
IMXBs with initially more massive donors (> 4 M_sun) encounter a delayed
dynamical instability; they are unlikely to survive this rapid mass transfer
phase. We determine limits for the age and initial parameters of Cygnus X-2 and
calculate possible dynamical orbits of the system in a realistic Galactic
potential, given its observed radial velocity. We find trajectories which are
consistent with a progenitor binary on a circular orbit in the Galactic plane
inside the solar circle that received a kick velocity < 200 km/s at the birth
of the neutron star. The simulations suggests that about 7% of IMXBs receiving
an arbitrary kick velocity from a standard kick velocity spectrum would end up
in an orbit similar to Cygnus X-2, while about 10% of them reach yet larger
Galactocentric distances.
