The Distributed Activation Energy Model (DAEM), used for the pyrolysis of a range of materials (including coal, biomass, residual oils and kerogen), assumes that the thermal decomposition of numerous components is described by a distribution of activation energies. Existing theories are reviewed with particular focus on methods used to evaluate solutions quickly and efficiently. This paper demonstrates that previous approaches taken to simplify the methods of solution can usually be identified as belonging to one of two distinct and physically relevant regimes. A careful analysis in these two regimes is given based upon asymptotic expansions, leading to systematic methods for rapidly finding accurate approximations. The new theory results in simple expressions for the devolatilisation rate of a given distribution of reactants. The method thereby provides a rapid and highly effective method for estimating kinetic parameters and the distribution of activation energies. Comparison of the simplified results with existing theories and with calculations of the full model are given. The methods provide a useful basis for calculations of coupled models of volatilisation and combustion, and for models with spatially varying temperatures. (C) 2003 The Combustion Institute. All rights reserved.