We have investigated the mechanism of exciton-exciton annihilation in organic lanthanide complexes by measuring the excitation density dependence of photoluminescence yield in neat films of a model europium chelate. The observed luminescence efficiency reduction at high excitation intensities has been attributed to the operation of the mutual annihilation of the ligand singlet excitons. The second order interaction rate constant, the exciton diffusivity, and the singlet exciton diffusion length in this material have been determined. These results were used to evaluate the role of exciton annihilation in organic light emitting diodes, lanthanide-based organic lasers, and light up-converters. Indications concerning the optimization of the performances of such devices have also been given.