Some rheokinetic studies of free radical polymerization have been published in the past. They generally make modeling of the time dependent increase of viscosity possible at low degrees of conversion, where Newtonian behavior holds and the rheokinetic equations can be linearized. In this paper we try to extend the rheokinetic approach to the region of high degrees of conversion, where the reacting solution is non-Newtonian and the shear rate at which the polymerization is performed becomes a fundamental parameter. Moreover, nonlinear phenomena such as the Trommsdorff effect and phase separations are likely to occur. The principal result of this study is that the Trommsdorff effect is reduced and sometimes eliminated when the polymerization is performed at high shear rate. Instabilities of the time dependent increase of viscosity occurred when the conversion was higher than 85%. They were attributed to phase separation of the macromolecules under shear flow.