One generally considers the conducting filament in ZnO-based valence change memristors (VCMs) as an aggregation of oxygen vacancies. Recently, the transmission electron microscopy observation showed the filament is composed of a Zn-dominated ZnOx. In this study, careful analysis of the temperature dependence of the ON state resistance demonstrates that the formation/rupture of a Zn filament is responsible for the resistive switching in ZnO VCMs. Cu/ZnO/Pt memristive devices can be operated in both VCM and ECM (electrochemical metallization memristor) modes by forming different metal filaments including Cu, Zn and a coexistence of these two filaments. The device operation can be reversibly switched between ECM and VCM modes. The dual mode operation capability of Cu/ZnO/Pt provides a wide choice of select devices for constructing memristive crossbar architectures.