In this work the optical spectroscopy and the energy transfer processes involving the Tb3+and Tm3+ ions, have been studied in eulytite double phosphate hosts of the type Sr3Y(PO4)3 doped with various amounts of the two Ln ions. It has been found that several energy transfer and cross-relaxation processes are active in this class of materials, upon excitation in the 5D4 level of Tb, and in the 1G4 one of Tm. In particular, a Tb→Tm transfer of excitation has been found to quench strongly the 5D4 level of Tb. This process occurs with a transfer efficiency increasing from 0.08 to 0.62, for a donor concentration of 2 mol%, and an acceptor concentration increasing from 2 to 15 mol%. The emission spectra are strongly affected by the presence of Tb⟷Tm energy transfer, and Tm→Tm cross relaxation processes.