  In this paper we present calculations of period distribution for old
accreting isolated neutron stars (INSs).
  At the age about a few billions years low velocity INSs come to the stage of
accretion. At that stage their period evolution is governed by magnetic
breaking and accreted angular momentum. Due to turbulence of the interstellar
medium (ISM) accreted momentum can both accelerate and decelerate rotation of
an INS and spin evolution has chaotic character.
  Calculations show that for constant magnetic fields INSs have relatively long
spin periods, $\ge 10^4$--$10^5$ s, depending on parameters of INSs and an ISM.
Due to long periods INSs have high spin up/spin down rates, which should
fluctuate on a time scale about a few years.
