A general, but simple, analytical technique is proposed for the solution of diffusion-controlled reaction problems (as, for example, occur during the photo-oxidation of polymers). With this technique the stationary concentration and reaction rate profiles can be calculated for arbitrary reaction kinetics and concentration dependent diffusion coefficients. As an example, the photo-oxidation of polyolefins is considered, which involves complex, concentration dependent, reaction kinetics. Excellent agreement between the analytical approximation and the numerical solution is obtained. Further, an analytical expression for the degradation profile (extend of reaction) is derived, which includes the starting-up effect. It is shown that owing to instationary effects, the degradation profiles obtained with artificial weathering tests may differ considerably from those obtained with outdoor weathering experiments. It is therefore suggested that artificial weathering tests be used to measure the reaction rate parameters and calculate the degradation profile rather than measuring the degradation profile directly.