Estimations are made of the critical concentration of energy-acceptor ions for which the average efficiency of the excitation transfer from energy-donor ions is 1/2. This gives a measure of the activator concentration at which Inokuti and Hirayama's theory is no longer applicable. Study is also made of the dominant multipole interaction responsible for the energy transfer between rare earth ions in inorganic solids. Finally, importance of the J -selection rule in the determination of the dominant interaction term in the resonance transfer and cooperative processes is emphasized.