  The properties of wind accretion in symbiotic X-ray binaries (SyXBs)
consisting of red-giant and magnetized neutron star (NS) are discussed. The
spin-up/spin-down torques applied to NS are derived based on a hydrodynamic
theory of quasi-spherical accretion onto magnetized NSs. In this model, a
settling subsonic accretion proceeds through a hot shell formed around the NS
magnetosphere. The accretion rate onto the NS is determined by the ability of
the plasma to enter the magnetosphere.Due to large Reynolds numbers in the
shell, the interaction of the rotating magnetosphere with plasma initiates a
subsonic turbulence. The convective motions are capable of carrying the angular
momentum through the shell. We carry out a population synthesis of SyXBs in the
Galaxy with account for the spin evolution of magnetized NS. The Galactic
number of SyXBs with bright (M_v<1) low-mass red-giant companion is found to be
from \sim 40 to 120, and their birthrate is \sim 5\times 10^{-5}-10^{-4} per
year. According to our model, among known SyXBs, Sct X-1 and IRXS
J180431.1-273932 are wind-fed accretors. GX 1+4 lies in the transition from the
wind-fed SyXBs to SyXBs in which the giants overflow their Roche lobe. The
model successfully reproduces very long NS spins (such as in IGR J16358-4724
and 4U 1954+31) without the need to invoke very strong magnetic fields.
