An interesting competition between two anti-Stokes emissions has been observed and interpreted in ZBLAN and fluoroaluminate (ALF) glasses activated by Ho 3+ and Nd 3+ ions, respectively. The intensity of an emission line situated spectrally close to the excitation wavelength, was seen to increase with temperature, whereas the intensity of another, upconverted emission line, in the same conditions, was seen to decrease. Both effects are believed to be caused by the same mechanism, which we have identified as the anti-Stokes multiphonon excitation of the state responsible for the first emission, followed by upconversion of the ESA (excited state absorption) or an energy transfer type process. Analysis of the kinetics of the observed effects enabled us to fit a theoretical model to the experimental data. It appears likely that the described competition may be a universal feature not restricted to the materials described in this work.