Peroxides react with polymers in a variety of ways. The fundamental comprehension and prediction of pertinent kinetics of reactions is consequently indispensable. Based on the mechanisms of reactions of cross-linking process, a new theoretical kinetic model framework was developed. The kinetic model was then applied to the reactions of cross-linking process of various peroxides and a chosen complex polymer compound, namely partially hydrogenated poly(acrylonitrile-co-1,3-butadiene). Whereas the initial macromolecular backbone structure was determined utilizing attached proton test carbon nuclear magnetic resonance, the evolution of overall concentration of cross-links was monitored through viscoelastic characteristics of the system. The model demonstrated good agreement with experimentally measured data and, moreover: the evolution of concentrations of various crucial species inherent to the cross-linking process were predicted. The most significant advantage of the developed kinetic model is that it may be readily applied to an assortment of polymer/peroxide systems. (c) 2011 Elsevier B.V. All rights reserved.