Memristors are expected to be one of the key building blocks for the development of new bio-inspired nanoelectronics. Memristive effects in transition metal oxides are usually linked to the electromigration at the nanoscale of charged oxygen vacancies (OV). In this paper we address, for Pt/TiO x /TaO y /Pt devices, the exchange of OV between the device and the environment upon the application of electrical stress. From a combination of experiments and theoretical simulations we determine that both TiO x and TaO y layers oxidize, via environmental oxygen uptake, during the electroforming process. Once the memristive effect is stabilized (post-forming behavior) our results suggest that oxygen exchange with the environment is suppressed and the OV dynamics that drives the memristive behavior is restricted to an internal electromigration between TiO x and TaO y layers. Our work provides relevant information for the design of reliable binary oxide memristive devices.