Ultrasonic velocities and attenuation in GaAs and HgTe have been measured between 2 K and room temperature in the frequency range 40 to 750 MHz. An experimental evaluation has been made of the pulse-superposition technique used for measuring the ultrasonic velocities, and particular attention has been paid to determination of the uncertainties involved. A correlation has been found between the ultrasonic pure mode elastic constant combinations of GaAs, HgTe and other III-V and II-VI zinc-blende structure compounds and the group IV elements. The elastic constant temperature dependences are well represented by a phenomenological model based on the Debye phonon frequency spectrum; differences between the model and experimental temperature dependences for the two compounds are compared. The ultrasonic attenuation in GaAs is dominated by damping due to ultrasonic phonon-thermal phonon interactions. The results are interpreted on the basis of the Woodruff and Ehrenreich model and the detailed nature of the phonon-coupling Gruneisen parameter is examined. Two main mechanisms contribute to the low-temperature attenuation in HgTe: phonon-phonon damping and dislocation-resonance damping. A large attenuation peak below liquid nitrogen temperature is explained in terms of thermal unpinning of dislocations.