The temperature dependence of the EPR spectrum of randomly oriented nitroxide radicals doped into nitrocellulose, polyurethane, and mixed nitrocellulose-polyurethane systems has been used to measure the temperature dependence of the motional correlation time during the glass-to-rubber transition. The correlation time for motion of the probes is obtained from the inward shift of the extrema lines using theories of slow tumbling, and is shown to follow an Arrhenius temperature dependence. The energy barriers to the motion are estimated.