The specific heats of Ge, Si, and Ge‐Si alloys were determined in the temperature range 300° to 1000°K, by a novel temperature‐modulation technique. The specific heat at constant pressurecpexceeds appreciably the Dulong‐Petit valuecDPat high temperature. Above the Debye temperature &thgr;Dthe divergence can be represented bycp/cDP=0.95+&agr;T/&thgr;DwhereTis the absolute temperature and &agr;=0.081 is a coefficient independent of alloy composition. This result is in disagreement with the current theory of the anharmonic contribution to the specific heat at high temperatures, which predicts &agr;=0.016 for Ge, and &agr;=0.030 for Si.