The distribution of the electrostatic potential across the electroactive-polymer film between the metal electrode and the solution has been analysed theoretically at various charging levels. The content of the film is determined by the electronic equilibrium with the metal and the exchange by co- and counterions with the solution. The electronic and ionic concentrations inside the film are assumed to be well below their saturation values. Two limiting shapes of the potential profile have been found, with a plateau region inside the film separating two space-charge layers near the interfaces, and with the potential drop distributed within the whole film, like that in an insulating film. In its turn, profiles with the bulk-film region have been separated into three different types, referred to as the "membrane", "electron-counterion" and "semiconductor" forms. Depending on the electronic and ionic parameters of the system, the profile may show various scenarios of evolution among these states upon sweeping the electrode polarization. Available ways to distinguish between these variants are discussed.