Single crystals of CaWO(4) and CaMoO(4) doped with Tb(3+) have been grown by the flux growth method. Their luminescence properties have been investigated in the 10-600 K temperature range under different experimental conditions. In spite of very similar spectra at low temperature upon excitation at 365 nm, the crystals show a very different behavior as the temperature is raised or the excitation wavelength is changed. These differences have been accounted for on the basis of models that take into consideration the position of the energy levels of the rare earth relative to the bandgap of the host material.