Redox-based nanoionic resistive memory cells are one of the most promising emerging nanodevices for future information technology with applications for memory, logic and neuromorphic computing. Recently, the serendipitous discovery of the link between redox-based nanoionic-resistive memory cells and memristors and memristive devices has further intensified the research in this field. Here we show on both a theoretical and an experimental level that nanoionic-type memristive elements are inherently controlled by non-equilibrium states resulting in a nanobattery. As a result, the memristor theory must be extended to fit the observed non-zero-crossing I-V characteristics. The initial electromotive force of the nanobattery depends on the chemistry and the transport properties of the materials system but can also be introduced during redox-based nanoionic-resistive memory cell operations. The emf has a strong impact on the dynamic behaviour of nanoscale memories, and thus, its control is one of the key factors for future device development and accurate modelling.