Accretion changes drastically both the magnetic and spin evolution of
neutron stars belonging to binary systems. Heating caused by accretion
decreases the conductivity of the neutron star crust and accelerates
the magnetic field decay if the currents maintaining this field are co
ncentrated in the crust. The present paper considers this mechanism of
the accretion-driven field decay in the case of accretion from the st
ellar wind of a companion. Such type of accretion is characterized by
lower accretion rates (10(-12)M./yr greater than or equal to M greater
than or equal to 10(-16) M./yr) comparing with accretion due to Roche
-lobe overflow. The field decay accompanying the wind accretion is sub
stantially slower but, nevertheless, it can strongly reduce the field
strength of the neutron star because in some binaries the duration of
the wind accretion phase is as long as similar to 10(9) yr. An influen
ce of the wind on the spin evolution seems to be less pronounced. Our
computations show that the neutron star cannot reach periods shorter t
han similar to 0.5 seven for a long accretion phase.