We use inelastic neutron scattering to demonstrate that the low-freque
ncy magnetic fluctuations in YBa2Cu3O6.6 (T-c = 62.7 K) change from co
mmensurate to incommensurate on cooling with the incommensurability fi
rst appearing at temperatures above T-c. For the energies studied, the
susceptibility at incommensurate positions increases on cooling below
T-c, accompanied by a suppression of the spin fluctuations at the com
mensurate points. These results suggest that incommensurate spin fluct
uations may be a common feature for all cuprate superconductors.