For an ageing process involving the consumption of a small molecule (typically O2 or H2O) by reaction with the polymer, there are critical conditions of reaction rate and/or thickness above which the process becomes kinetically controlled by the diffusion of the small molecule in the polymer. Suitable lifetime prediction models must then involve the thickness distribution of reaction products. This latter can be predicted from Fick’s law, modified by a term relative to the rate of consumption of the diffusing species by the chemical reaction. Some problems related to the use of this approach are examined here. It appears that, in the most frequent case, the thickness of the degraded layer is of the order of magnitude of D/k, where D is the diffusion coefficient and k the pseudo-first-order rate constant for reactant consumption. Some examples of application related to photochemical, radiochemical and thermochemical ageing are examined. It can, for instance, be shown that in photochemical or radiochemical ageing, the thickness of the oxidized layer (TOL) is proportional to the reciprocal of I(beta), where I is the radiation intensity and beta an exponent depending essentially on the radical chain mechanism. It is generally expected that in the case of thermal ageing, the TOL is a decreasing function of the temperature. Some consequences of diffusion control on accelerated and natural ageing methods are briefly examined. The consequences of the ageing-induced "skin-core" structure due to the diffusion control are examined. The main features of the observed polymer embrittlement can be explained in terms of fracture mechanics.