The emission and excitation spectra as well as the decay kinetics of cerium-doped fluoro-hafnate glasses of various compositions have been studied using vacuum ultraviolet synchrotron radiation excitation. It has been found that iso-valent modifications of the glass composition do not strongly affect the decay kinetics of cerium emission while two-valent oxygen ions create additional quenching centres leading to a decrease of the light yield. It has been shown that the quenching of Ce emission in cerium-doped fluoro-hafnate glasses starts with a process of impact excitation of cerium emission centres. The results show that the dominant mechanism of energy transfer from the matrix to cerium emission centres in fluoride glasses is different for the 315 nm band and the 400 nm band.