Elastic compliance measurements are reported in KTa1-xNbxO3 mixed crystals exhibiting a concentration-dependent ferroelectric phase-transition temperature Tc. For concentrations x0.008, an anomaly is observed at Tc in the temperature dependence of the elastic compliance s11, consisting of a steplike discontinuity with a superimposed Curie-Weiss-type singularity. The critical exponent, defined by s11(T-Tc)-, varies from =1.3 for x=0.05 to =1.9 for x=0.008. As x is lowered towards 0.008, the amplitude of the step discontinuity is largely unaffected. For x<0.008, no anomaly occurs. The experimental results are compared to dielectric data sets previously obtained, and interpreted in the light of renormalization-group predictions. A specific quantum critical behavior is obtained for transition temperatures Tc<30 K. © 1983 The American Physical Society.