In Part I of this work, experimental data showed that the effect of low concentrations of free radical initiator injected into polyethylene during extrusion depended upon the degree of unsaturation and branching in the feed as well as the molecular weight. This paper shows attempts to quantitatively explain these reactive extrusion results through development of two kinetic models based upon the rate equations for reactions considered dominant. The first model developed incorporated unsaturation via consideration of simultaneous crosslinking-endlinking reactions. It contains two variable parameters : the overall initiator efficiency and a ratio of two rate constants reflecting the reactivity of the unsaturated bonds. The model was able to fit the changes in molecular weight distribution of both the low density and linear low density polyethylene but not the high density polyethylene samples. In addition to fitting the molecular weight distribution, this model also provided reasonable values of initiator efficiencies for crosslinking, endlinking, and chain extension reactions, as well as the number of terminal vinyls of the products. The second model is a special case of the first : it neglects the presence of unsaturation in the feed. This second model is actually the usual "crosslinking" model widely known from a derivation based upon statistical arguments. It was not able to fit most molecular weight distributions obtained. However, the model was shown to be useful for accounting for observed molecular weight distribution for a high density polyethylene sample of low initial unsaturation. Also, it was able to explain the amount of gel formed as a function of initiator concentration.