Stability is one of the most important characteristics of electrocatalysts used in low-temperature fuel cells with a proton exchange membrane. The corrosion-morphological stability of supported electrocatalysts containing platinum and platinum-copper nanoparticles with ~20 wt % Pt was evaluated under the conditions of voltammetry stress testing corresponding to different degradation mechanisms. The effect of the difference in the architecture of Pt–Cu nanoparticles on the stability of catalysts and changes in their composition as a result of stress tests were studied. At close values of the electrochemically active surface area (ECAS), the carbon-supported bimetallic catalysts demonstrated significantly higher stability compared to the commercial Pt/C catalysts. The Pt(Cu)/C catalyst obtained by sequential deposition of copper and platinum showed the highest resistance to the degradation and selective dissolution of copper during the testing.