The dynamical properties of two spin systems composed of conduction electron spins and localized d-spins interacting by exchange are investigated in connection with the electron-spin resonance of d-spins with the free electron g-value. It seems to us that some basic onsiderations are necessary for the problem along the line of the widely accepted idea that the s-d' interaction itself does not lead to any relaxation time and shift. The usual adiabatic approximation is applied to this idea. A modified damping equation of the Bloch type as well as Bloch's relaxation theory are also useful, but these are not enough for a complete solution of the problem. A certain controversy involved in recent experimental and theoretical work at Berkeley concerning the electron spin resonancein Cu-Mn dilute alloy is pointed out and examined. We believe that the possibility could not be eliminated that the spin-lattice relaxation time of conduction electrons in the alloy due to mechanisms other than the s-d' interaction is longer than previous authors have assumed.