The nonexponential response of propylene carbonate and glycerol near their glass transitions could be selectively altered using nonresonant spectral hole burning (NSHB) experiments. This observation provides evidence of the existence of a distribution of relaxation times in these supercooled liquids. NSHB is based an a pump, wait, and probe scheme and uses low-frequency large amplitude electrical fields to modify the dielectric relaxation. The temporal evolution of the polarization of the sample is then measured subsequent to a small voltage step. By variation of a recovery time inserted between pump and probe, the refilling of the spectral features could be monitored and was found to rake place on the time scale set by the peak in the distribution. The recovery time and pump frequency dependences of the spectral modifications were successfully simulated using a set of coupled rate equations. (C) 1997 American Institute of Physics.