The physics underlying the dynamics of molecules near their glass temperature, T-g, comprises one of the major unsolved problems in condensed matter. Of particular interest are the striking changes in relaxation properties observed at temperatures similar to1.2 times higher than T-g. Herein, we describe experiments in which these changes in dynamics are induced by pressure variations. For several supercooled liquids, the relaxation time associated with the change in dynamics is found to be invariant to both temperature and pressure. That is, the time scale of the molecular motions determines the onset of strong intermolecular cooperativity and the accompanying dynamical changes. While thermodynamic variables such as temperature and pressure influence the crossover in dynamics, the governing variable is the time scale. (C) 2003 American Institute of Physics.