Four bands, all belonging to the main thallium centre, are detected in the tripler luminescence spectrum of thallium-doped cesium halides under excitation in impurity absorption bands. Their spectral, polarization and kinetics characteristics are studied at 0.35 to 360 K. The parameters of the corresponding relaxed excited states (RES) minima are calculated. Two ultraviolet emission bands are ascribed to electronic transitions from trigonal and tetragonal Jahn-Teller minima of the triplet RES of Tl+ ion. Two visible bands are assumed to arise from two different off-centre configurations of a self-trapped exciton perturbed by Tl+ ion.