Direct measurements of longitudinal (d33) and transverse (d31) piezoelectric coefficients have been made on cuboid samples of C-poled 0.955Pb[Zn1/3Nb2/3]O3-0.045PbTiO3 (PZN-4.5PT) and 0.68Pb[Mg1/3Nb2/3]O3-0.32PbTiO3 (PMN-32PT) single crystals. The measurements were made in a Berlincourt-type press over a wide range of dynamic and static bias stresses. In the transverse mode, the response was found to be essentially anhysteretic and d31 was independent of the dynamic stress amplitude. In contrast, for the longitudinal mode, the piezoelectric charge-stress behavior is hysteretic. Moreover, the relative hysteresis size and the d33 coefficient are both strong functions of bias stress, dynamic stress amplitude, and frequency; coupling of the dynamic stress dependency of d33 to the charge-stress hysteresis is demonstrated by a quasi-Rayleigh-type relationship. The observed hysteretic response could be due to domain switching in the crystals although this would be unexpected for a C-poled rhombohedral crystal. Instead, following the observed difference between transverse and longitudinal behaviors, it is suggested that polarization rotation away from the poling direction leads to a hysteretic response. © 2004 American Institute of Physics.