The concept of an asymmetric FeWO4/MnO2 electrochemical capacitor cycled in a neutral aqueous electrolyte is presented for the first time. Commercially available cryptomelane-type MnO2 and synthesized nanocrystalline FeWO4 were used as positive and negative electrode materials, respectively. Prior to assembling the cell, the electrodes have been individually tested in a 5 M LiNO3 electrolyte solution to define both the adequate balance of active material in the supercapacitor and the proper working voltage window. Then, the full asymmetric device has been cycled between 0 and 1.4 V for over 40,000 cycles and subjected to accelerated ageing tests under floating conditions at different voltages, without any significant change on its electrochemical behavior. This remarkable stability shows the interest of developing full oxide-based asymmetric supercapacitors operating in non-toxic aqueous electrolytes that could compete with commercial carbon-based electrochemical double-layer capacitors.