The anti-Stokes fluorescence excitation with a monochromatic source can be due to three mechanisms: the successive absorptions, the energy transfer and the photon avalanche distinguishable by certain experimental tests specified by the theoretical study of a three-level model. The photon avalanche is characterized by the existence of a threshold for the excitation density with, beyond this threshold, a sudden increase of the anti-Stokes fluorescence intensity and by a rise time which may be longer than the storage level lifetime, with a strongly marked bending point. This process, efficient for the population inversion, is not separable from the other two mechanisms which can favour it, impede it or even block it. Thus, the avalanche can be started by a weak ground-state absorption and blocked when this absorption becomes too strong. Then, a system based on an excited-state absorption has two operating modes: a successive absorptions mechanism and the photon avalanche. The transition from the former mode to the latter progressively occurs as the excited-state absorption increases compared with the groundstate absorption. The energy level diagram of Tm3+ ion favours the excited-state absorption processes, with, in particular the photon avalanche. Some experimental results concerning Tm3+ in fluoride crystals are given.