  We derive the kinetic equations for the hopping transport that take into
account electron spin and the possibility of double occupation. In the Ohmic
regime the equations are reduced to the generalized Miller-Abrahams resistor
network. We apply these equations to the problem of the magnetic moment
relaxation due to the interaction with the random hyperfine fields. It is shown
that in a wide range of parameters the relaxation rate is governed by the hops
with the similar rates as spin precession frequency. It is demonstrated that at
the large time scale spin relaxation is non-exponential. We argue that the
non-exponential relaxation of the magnetic moment is related to the spin of
electrons in the slow-relaxing traps. Interestingly the traps can significantly
influence the spin relaxation in the infinite conducting cluster at large
times.
