  Different accretion regimes onto magnetized NSs in HMXBs are considered:
wind-fed supersonic (Bondi) regime at high accretion rates $\dot M\gtrsim
4\times 10^{16}$~[g s$^{-1}$] , subsonic settling regime at lower $\dot M$ and
supercritical disc accretion during Roche lobe overflow. In wind-fed stage, NSs
in HMXBs reach equilibrium spin periods $P^*$ proportional to binary orbital
period $P_b$. At supercritical accretion stage, the system may appear as a
pulsating ULX. Population synthesis of Galactic HMXBs using standard
assumptions on the binary evolution and NS formation is presented. Comparison
of the model $P^*$ -- $P_b$ (the Corbet diagram), $P^*$ -- $L_x$ and $P_b$ --
$L_x$ distributions with those for the observed HMXBs (including Be X-ray
binaries) and pulsating ULXs suggests the importance of the reduction of $P^*$
in non-circular orbits, explaining the location of Be X-ray binaries in the
model Corbet diagram, and the universal parameters of pulsating ULXs depending
only on the NS magnetic fields.
