Electrodeionisation is the combination of electrodialysis and ion exchange processes where ion exchangers are disposed between the membranes. The main application actually is water deionisation. We develop a theory for electrodeionisation based on the well-known equilibrium theory of ion exchange columns. In the differential mass balance equation for ion exchange columns, a term is added accounting for mass transport through the membrane. The second equation is the ion exchange isotherm. The system is solved by the method of characteristics. Several cases are considered depending of the membrane flux law. Transient and steady states are studied. During transient state an ion exchange front develops and propagates through the bed with a downstream plateau of non-constant concentration and an upstream concentration varying exponentially. An interesting result is shown: at steady state, there is no influence of the ion exchange isotherm. The electrical properties of the ion exchanger only influence the process. Several aspects of the model are discussed: non-linear isotherm, transversal concentration gradient, axial dependant flux.