A method of rheokinetic analysis is applied to free-radical polymerization of acrylamide in a water solution initiated by an oxidizing reducing system. The special feature of this system is the second-order kinetics of the initiation stage. Theoretical analysis predicts the main effects, such as the time dependence of viscosity and the degree of polymerization, concentration influence of a monomer and an initiator, and the temperature dependence of the viscosity profile at different experimental conditions. Experimental data confirmed the idea about the second-order reaction of initiation. Observed dependencies were close to theoretical predictions. Rate constants of different individual stages of a reaction and "apparent" values of activation energy were found and compared with published values. The possibility of solving an inverse rheokinetic problem from viscometric data was confirmed.