In this paper we have theoretically discussed two kinds of the ways for enhancing radiation crosslinking of polymers, that is: (1) a second unit which crosslinks more easily is introduced into a linear polymeric chain, (2) a reactive polyfunctional monomer is mixed with a linear polymer before irradiation. According to the first model of enhanced crosslinking, the chain structure of the polymer can be described by,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767474&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767467&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767478&type=,where A and B are the units which react at different rates. During irradiation three crosslinking structures may be formed as follows:,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767484&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767488&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767471&type=,If the rates forming the structures of Type (Ⅱ) and (Ⅲ) are greater than that of Type(Ⅰ), we say that B has an enhancing effect on the radiation crosslinking of linear polymers with the main structural units of A. For instance, the radiation crosslinking of polydimethylsiloxane containing some methylvinylsiloxane units is of this model. On the basis of the elementary laws of probability, two general relations between sol fraction,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767506&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767516&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767509&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767502&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767538&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767535&type=,where W,1, is the weight fraction of i-mers of the initial polymers, X,A, and X,B, are the number fractions of A and B, q,A, and q,B, are the number fractions of crosslinked units of Type A and B, S is the sol fraction, and ,φ, is the probability that a crosslinked unit selected at random links up with the finite chains through a crosslink bridge.,Considering the second model of enhanced crosslinking, for the mixture systems of a linear polymer and a bifunctional monomer the radiation may induce the crosslinking reactions of following two main types:,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767526&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767530&type=,http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=42767528&type=,where C—C is the bifunctional monomer,k,AA, and ,k,AC, are the rate constants of two different crosslinking reactions. If ,k,AC,>,k,AA, the bifunctional monomer has an enhancing effect on the radiation crosslinking of polymers composed of the structural units of A. Those polymers, such as polyethylene, polydimethylsiloxane and others, mixed with a reactive bifunctional monomer like ethylene glycol dimethacrylate can be irradiated to crosslink in such a way. Regarding X,B, the ratio of the numbers of bifunctional groups to that of the structural units of polymers, then, Eqs. (1) and (2) may also be applicable to the second model.,From Eqs. (1) and (2) three special cases of the molecular weight distributions of initial polymers, namely uniform, Flory's and Schulz-Zimm's, are discussed.