It is shown that the unusual observed saturation behavior of the microwave electron spin resonance associated with F centers in KCl, NaCl, and KBr crystals can be accounted for if the overall width is ascribed to interaction between the F-center electrons and the nuclear magnetic moments of the ions adjacent to the F centers. The measured saturation factor gives for F centers in KCl a spin-lattice relaxation time of 2.5×10-5 sec at room temperature. The observed saturation behavior in which only the absorption saturates is in marked disagreement with the Kramers-Kronig relations. However it is shown, that the Kramers-Kronig relations are not applicable to saturated systems. Expressions which avoid the use of these relations are presented for saturable systems.