Inelastic neutron scattering measurements ofLa1.85Sr0.15CuO4andYBa2Cu3O7show that the dispersion of the high energy LO phonon mode along the (1,0,0) direction is strongly temperature dependent, and at low temperatures develops an anomalous feature indicative of dynamic cell-doubling. The anomaly does not change through superconducting transition and gradually disappears between 50 and 250 K in LSCO. Possible implications are discussed. ©1999 American Institute of Physics.