Acoustic wave velocities have been measured in RbCl and CsCl to 17 GPa. The compressional wave velocities vary with density as Vp (km/s)=3.4143 (84)+1.368 (11) Δ&rgr; for the high-pressure phase of RbCl and Vp (km/s)=2.8247 (57)+1.1469 (77) Δ&rgr; for CsCl (numbers in parentheses indicate uncertainties on the last digit). The equations of state of RbCl and CsCl have also been determined at room temperature to ~30 GPa. Eulerian finite strain equation of state parameters are &rgr;02=3.3068 (10) Mg m-3, K0T=17.9 (10) GPa and K'0T=5.23 (29) for RbCl in the B2 structure, and K0T=17.01 (29) GPa and K'0T=5.49 (15) for CsCl. The accumulated set of data for the alkali chlorides under high pressure is used to test several empirical relations between velocity and density. A simple logarithmic relation is shown to allow the most accurate extrapolation from low-pressure velocity data. Gruneisen's parameters are also calculated from the velocity and density data, allowing a complete thermal equation of state to be developed for the alkali chlorides. ¿ American Geophysical Union 1994