In this work we give detail consideration of the possible scenario of evolution of isolated neutron stars ( INSs ) and determine some characteristics of X-ray pulsars from their spin period evolution .

The new points of our consideration are :

–we give additional arguments for the short time scale of the Ejector stage ( \approx 10 ^ { 7 } -10 ^ { 8 } yrs ) .

–we proposed specific SPINDOWN THEOREM and give some arguments for its validity .
Discovery of accreting INSs will means that the SPINDOWN THEOREM is true .

–we consider firstly evolution of spin period of a NS on the Accretor stage and predict that its period \geq 5 \cdot 10 ^ { 2 } sec and INSs can be observed as pulsating X–ray sources .

–we modeled accretion onto an INS from the interstellar medium in the case of spherical symmetry for different values of the magnetic field strength , ambient gas density and NS ’ s mass .
The periodic sources with P from several minutes to several months can appear .

–we consider new idea of stochastic acceleration of very old NSs due to accretion of turbulizated ISM .

–last point means that INSs can be spin up and spin down with equal probability .

–using the observed period changes for four systems : Vela X–1 , GX 301–2 , Her X–1 and Cen X–3 we determined D , the ’ diffusion coefficient ’ , –parameter from the Fokker–Planck equation .

–using strong dependence of D on the velocity for Vela X–1 and GX 301–2 , systems accreting from a stellar wind , we determined the stellar wind velocity .
For different assumptions for a turbulent velocity we obtained V = ( 660 - 1440 ) km \cdot s ^ { -1 } .

–we also determined the specific characteristic time scales for the ’ diffusion processes ’ in X-ray pulsars .
It is of order of 200 sec for wind-fed pulsars and 1000-10000 sec for the disk accreting systems .