  The spin dynamics of the strongly localized, donor-bound electrons in
fluorine-doped ZnSe epilayers is studied by pump-probe Kerr rotation
techniques. A method exploiting the spin inertia is developed and used to
measure the longitudinal spin relaxation time, $T_1$, in a wide range of
magnetic fields, temperatures, and pump densities. The $T_1$ time of the
donor-bound electron spin of about 1.6 $\mu$s remains nearly constant for
external magnetic fields varied from zero up to 2.5 T (Faraday geometry) and in
a temperature range $1.8-45$ K. The inhomogeneous spin dephasing time,
$T_2^*=8-33$ ns, is measured using the resonant spin amplification and Hanle
effects under pulsed and steady-state pumping, respectively. These findings
impose severe restrictions on possible spin relaxation mechanisms.
