The radiation-induced crosslinking of linear low density polyethylene chains has been analysed theoretically using an atomistic analysis and a Flory-Stockmayer (FS) analysis. Experimentally, gel fractions greater than the theoretical maximum obtainable, assuming every radical reacts to form a crosslink (namely, D. G(R)/2), indicate the occurrence of chain-reactions both in the presence of acetylene and in vacuo. Based on previous studies, chain-reaction mechanisms are postulated, involving unterminated polyenes in acetylene and scission-generated vinyls in vacuo. Accordingly, numerical comparisons of the theoretical and experimental gel-fraction results, as a function of dose (D), have been used to calculate the number of ’gel-effective’ chain-steps per initial alkyl radical generated (N-CS,N-D) for both the atomistic and FS analyses. Both systems of analysis show that, as dose increases, N-CS,N-D for the acetylene and in vacuo results decrease from maximum values at or just after the gel points. The decay is interpreted as resulting from the increased probability of radical-radical termination reactions towards higher levels of dose. Although there are differences between the two analyses, both give essentially the same interpretation of the experimental results. The atomistic analysis predicts maximum values of N-CS,N-D of 9.0 in the presence of acetylene and 2.9 in vacuo. The corresponding values from the FS analysis are 9.4 and 2.8 respectively. As the dose is increased further, the atomistic analysis gives 2.1th- and 2.6th-order decays of N-CS,N-D as functions of the dose, for the acetylene and in vacuo results respectively. The FS analysis gives, correspondingly, 2.6th- and 2.8th-order decays. General equations are developed for irradiated polymers, which relate gel fraction to the dose and the number of initial radicals generated in a pre-irradiated number-average degree of polymerization, via N-CS,N-D.