For a series of five amorphous polymers with a broad range of T-g values the kinetics of macroradical decay was measured by ESR technique and evaluated by the second-order kinetic model. It was found that the temperature T-tr of the transition between two regions of different reactivity in free radical decay reaction agrees quite well with the temperature parameter T-0 of the Vogel-Fulcher-Tamman-Hesse (VFTH) equation for alpha-segmental dynamics. This parameter represents the onset of alpha-segmental mobility in glassy state below T-g. A nontraditional way of the estimation of T-0 values for alpha-segmental dynamics through study of the macroradical decay in glassy state of amorphous polymers has been suggested.