Transition metal oxides, especially cobalt oxides and hydroxides, are of great interest as precious metal free electrode materials for the oxygen evolution reaction (OER) in electrochemical and photoelectrochemical water splitting. Here, we present detailed studies of the potential‐ and pH‐dependent structure and structural stability of Co₃O₄ and CoOOH in neutral to alkaline electrolytes (pH 7 to 13), using operando surface X‐ray diffraction, atomic force microscopy, and electrochemical measurements. The experiments cover the pre‐OER and OER range and were performed on epitaxial Co₃O₄ (111) and CoOOH(001) films electrodeposited on Au(111) single crystal electrodes. The CoOOH films were structurally perfectly stable under all experimental conditions, whereas Co₃O₄ films exhibit at all pH values reversible potential‐dependent structural transformations of a sub‐nanometer thick skin layer region at the oxide surface, as reported previously for pH 13 (F. Reikowski et al., ACS Catal. 2019, 9, 3811). The intrinsic OER activity at 1.65 V versus the reversible hydrogen electrode decreases strongly with decreasing pH, indicating a reaction order of 0.2 with respect to [OH − ]. While the Co₃O₄ spinel is stable at pH 13, intermittent exposure to electrolytes with pH≤10 results in dissolution as well as gradual degradation of its OER activity in subsequent measurements at pH 13.