Zinc oxide (ZnO) and materials based on it are often used to create battery-type supercapacitor electrodes and are considered as promising materials for hybrid asymmetric supercapacitors. However, when creating such electrodes, it is necessary to take into account the instability and degradation of zinc oxide in aggressive environments with a non-neutral pH. To the best of our knowledge, studies of the changes in the properties of ZnO-containing electrodes in alkaline electrolytes have not been carried out. In this work, changes in the structure and properties of these electrodes under alkaline treatment were investigated using the example of ZnO-containing composites, which are often used for the manufacturing of supercapacitor electrodes. Supercapacitor electrodes made of two materials containing ZnO were studied: (i) a heterogeneous ZnO-Co3O4 system, and (ii) a hexagonal h-Zn-Co-O solid solution. A comparison was made between the structure and properties of these materials before and after in situ electrochemical oxidation in the process of measuring cyclic voltammetry and galvanostatic charge/discharge. It has been shown that the structure of both nanoparticles of the heterogeneous ZnO-Co3O4 system and the h-Zn-Co-O solid solution changes due to the dissolution of ZnO in the alkaline electrolyte 3.5 M KOH, with the short-term alkaline treatment producing cobalt and zinc hydroxides, and long-term exposure leading to electrochemical cyclic oxidation–reduction, forming cobalt oxide Co3O4. Since the resulting cobalt oxide nanoparticles are immobilized in the electrode structure, a considerable specific capacity of 446 F g−1 or 74.4 mA h g−1 is achieved at a mass loading of 0.0105 g. The fabricated hybrid capacitor showed a good electrochemical performance, with a series resistance of 0.2 Ohm and a capacitance retention of 87% after 10,000 cycles.