The modelling of the full molecular weight distribution in addition polymerisation gives rise to very large dimension (10(3)-10(6)) systems of ordinary differential equations, often exhibiting serious stiffness issues. This article summarises a methodology recently implemented by our group, in which the QSSA is applied on the fast dynamic species in order to reduce the stiffness, and then the remaining equations are solved by computationally inexpensive explicit algorithms (such as Euler). Specific features of the methodology are illustrated by application to the academically and industrially relevant systems of controlled radical polymerisation (RAFT and NMP cases) and coordination catalysis polymerisation. (C) 2012 Canadian Society for Chemical Engineering