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, T1, in a wide range of magnetic fields, temperatures, and pump densities. The T1 time of the donor-bound electron spin of about 1.6 µs 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.