The attenuation and phase velocity variation of longitudinal and transverse ultrasonic waves have been measured in the fluorozirconate glass 57.5 % ZrF 4, 33.75 % BaF2 and 8.75 % ThF4, in the temperature range 0.08 to 250 K. The usual behaviour of amorphous insulators has been observed at the lowest temperatures indicating the existence of two-level tunnelling systems (TLS). From these acoustic measurements not only the coupling constants between TLS and longitudinal and transverse acoustic waves, but also the TLS density of states have been determined