Polymers have become immensely important in industrial development. They are nowadays used for vibration damping bearings in car manufacturing, shipbuilding, and civil engineering and in the production of tyres, but not only for these. Their good formability, processibility, flexibility, and adhesiveness have also long resulted in their application as coating materials, for example for solar voltaic cells, metal surfaces, electronic components, and now even for biocompatible coating of medical implants. The purpose of the polymeric coating is thereby to protect the underlying material against environmental influences and potentially damaging media. The ensurement of adequate protection requires a knowledge of the effective life and ageing behaviour of the polymeric material, however, which brings us to the subject of this contribution. Various ageing phenomena will be discussed and experimental methods will be presented which provide information on both the physical ageing behaviour of polymers as well as on a partial area of their chemical ageing behaviour. A phenomenological material model which is rheologically motivated and thermo-mechanically consistent will be derived from the experimental results which have been obtained. The model not only enables physical ageing processes to be described, but also allows thermo-oxidative ageing to be depicted as representative of a possible chemical ageing behaviour. The formulation of the one-dimensional model enables it to detect the glass transition region, which is an essential for physical ageing behaviour. It takes the chemically caused ageing phenomena of chain scission and network reformation into consideration without the need to resolve microscopic processes in detail.