The purpose of the paper is to clarify the mechanism of excitation energy transfer between unlike trivalent rare-earth ions in inorganic solids. We have measured the manner in which the intensities of the luminescences of Tb3+ (5D4→7F5) and Eu3+ (5D0→7F2) are quenched and the decay rates are made faster by the coexistence of other kinds of trivalent rare-earth ions as a result of energy transfer. As the host material, calcium metaphosphate glass was used. The combination of Tb3+ donor and Nd3+ acceptor was studied most in detail. The results are discussed in terms of the resonance theory of energy transfer, and the experimental data are analyzed using the numerical calculations of the theory recently made by Inokuti and Hirayama. The overlap integrals of donor emission spectra with acceptor absorption spectra were estimated from the data of spectral measurements. Among the resonance mechanisms due to various electrostatic multipole interactions, the dipole—quadrupole interaction gave the best fit between theory and experiment. The transfer due to the exchange interaction was inferred not to be operative. It has been finally concluded that the mechanism of the energy transfer between unlike trivalent rare-earth ions in inorganic solids is predominantly governed by the dipole—quadrupole interaction.