The invention relates to a process for the molecular weight increase/crosslinking of non-halogen-containing thermoplastic polymers, in which process a composition comprising a) a non-halogen-containing thermoplastic polymer; b) a functional compound having at least two unsaturated carbon bonds; and c) an alkoxyamine having a structural unit (I), which forms free radicals at the melting temperature/processing temperature of the polymer, is mixed and heated above the melting point of the polymer in the case of crystalline polymers or the softening point in the case of amorphous polymers. The invention relates also to the composition itself, to the use thereof in increasing the molecular weight of polymers and to polymers having increased molecular weight or crosslinked polymers prepared in accordance with that process