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Initial stages of copper electrocrystallization on glassy carbon from sulfuric acid electrolytes of pH 0.3 and 3.7 are studied by the cyclic voltammetry method on rotating and stationary ring–disk electrode. The rate of nucleation and growth of a metallic phase of copper in a 0.5 M Na2SO4 + 0.01 М CuSO4 (pH 3.7) solution is marginally higher than in a 0.5 M H2SO4 + 0.01 M CuSO4 acid electrolyte (pH 0.3). Regularities governing the multistage discharge of copper ions, the formation of the new phase nuclei, and the deposit dissolution are analyzed. No copper adlayers form on glassy carbon at potentials more positive than the equilibrium potential of a reversible copper electrode, the copper nucleation occurs via the Volmer–Weber mechanism. The oxygen-containing surface groups of glassy carbon (quinone–hydroquinone, carbonyl, etc.) are probably active centers for the discharge of copper ions and the nucleation of the new phase. The results of the study are compared with the data on the kinetics of copper electrocrystallization on a platinum electrode.