In this thesis a new approach for characterisation of digital mobile radio channels is investigated. The new approach is based on recognition of the fact that while the fading which is characteristic of the mobile radio channel is very rapid, the processes underlying this fading may vary much more slowly. The comparative stability of these underlying processes has not been exploited in system designs to date. Channel models are proposed which take account of the stability of the channel. Estimators for the parameters of the models are proposed, and their performance is analysed theoretically and by simulation and measurement. Bounds are derived for the extent to which the mobile channel can be predicted, and the critical factors which define these bounds are identified. Two main applications arise for these channel models. The first is the possibility of prediction of the overall system performance. This may be used to avoid channel fading (for instance by change of frequency), or compensate for it (by change of the signal rate or by power control). The second application is in channel equalisation. An equaliser based on a model which has parameters varying only very slowly can offer improved performance especially in the case of channels which appear to be varying so rapidly that the convergence rate of an equaliser based on the conventional model is not adequate. The first of these applications is explored, and a relationship is derived between the channel impulse response and the performance of a broadband system.