The temperature dependence of the sound velocities for 13 propagation modes has been measured in a single crystal of Cu-Zn-Al monoclinic 1 8 R martensite, using the pulse-echo method. By numerical procedure the complete set of nine second-order adiabatic elastic constants ( C ij ) of the closest orthorhombic reference phase, their relative thermal variation ( Γ ij ) , and the Debye temperature ( θ D ) have been obtained. The values found in the martensitic phase have been compared to data avalaible for the high-temperature bcc β -phase in the same alloy system. The velocity surfaces in the corresponding crystallographic directions of both phases have also been computed at different temperatures. It has been shown that the mechanical stability of the lattice for some particular distortions decreases as the transformation temperature is approached in both the martensitic as well as in the β phase.