Combinatorial chemistry was applied to the optimization of (Gd2-x-yMx)O-3:Eu-y(3+) phosphors for displays. The (Gd2-x-yMx)O-3:Eu-y(3+) phosphor is a promising candidate for red field emission display (FED) phosphors. Screening was performed in terms of cathodoluminescence at a low voltage excitation and photoluminescence. We developed a ternary material library of a triangle-type composition array to obtain the optimum composition of co-dopants. Three co-dopants (Al, Ca, Mg) were introduced into Gd2O3:Eu3+.Gd2O3 was a good host material for red FED phosphors at a low voltage excitation, and the cathodoluminescent efficiency of Al co-doped phosphor, (Gd1.83Al0.05)O3:Eu-0.12(3+), was superior to that of the commercial red phosphor Y2O3:Eu3+. We also investigated the energy transfer between Eu3+ ions by analyzing the decay curves of emissions originating from D-5(0) energy states in terms of multipolar interactions. We can explain the quenching of emissions from D-5(0) in terms of a newly proposed cross relaxation in association with an intercenter diffusion.