A new approach to polymer pyrolysis kinetics is based on moments of a population balance equation describing chain-end and random scission and repolymerization. Two equations for the zero and first moments (moles and mass) are solved for isothermal and nonisothermal (linear T increase) thermogravimetric analysis. The isothermal case is shown to have a simple relationship to an empirical acceleratory model, thus revealing its limitations and approximations. With realistic values of prefactors and activation energies, the new theory compares well with experimental data for polyether-ether-ketone pyrolysis.