The relative fluorescence yield of vacuum-evaporated films of tris-(8-hydroxyquinolinato) aluminum (III) (Alq(3)) as a function of steady-state exciting light intensity has been measured. The yield decreases, due to singlet exciton-exciton interaction, with increasing intensities, to a half of the low-intensity yield at 5 x 10(21) ph/cm(2)/s. The second order singlet-singlet annihilation rate constant is found to be gamma(ss) = (1.1 +/- 0.5) x 10(-10) cm(3)/s. If the reaction is diffusion-limited, this rate implies an average singlet exciton diffusivity D-s = (6 +/- 2) x 10(-5) cm(2)/s, and permits to rule out singlet-singlet interaction as the reason for the observed large-current density roll-off in the electroluminescence efficiency of Alq(3)-based light emitting diodes. (C) 2004 Published by Elsevier B.V.