The free-radical polymerization of methyl methacrylate (MMA) at very high conversions (x > 0,8) was studied in the temperature range 60°C to 160°C. 2,2'-Azodiisobutyronitrile (AIBN) and benzoyl peroxide (BPO) were used as initiators. In the case of the latter, decomposition kinetics at very high monomer conversions was investigated, too. For temperatures T 5 120°C where depropagation can be neglected a simple kinetic model based on "reaction diffusion" and free volume theory was developed. The model contains only a single adjustable parameter, the critical free volume fraction V*. Good agreement between model predictions and experiments was obtained. v* is independent of initial initiator concentration and reaction temperature, and there is some evidence that V* is also independent of the chemical nature of the initiator.