The electrochemical behaviour of some Pb-Cu alloys (Cu = 0.008 - 0.06 %) in 5.0 M H2SO4 solutions was studied to explore the role of copper on the performance of grids of lead-acid batteries under different conditions. The results showed that the self-sulphation increased as Cu content increased due to the strong galvanic action between Pb and Cu. Potentiostatic results indicated that the passivity current (PbSO4 formation region), its critical value, and the oxygen evolution current decreased substantially in the presence of Cu, and the minimum values were observed for the alloy Pb-0.036 % Cu alloy. Hydrogen-overpotential was found to increase in the presence of Cu and also the maximum overpotential was observed for the alloy Pb-0.036 % Cu, but the overpotential for the alloy Pb-0.024 % Cu was even lower than that of Pb. The self-discharging process showed a strong dependence on Cu content where the self-discharging of Pb-0.036 % Cu was the fastest. The oxide formation efficiency was found to decrease in the presence of Cu, charging-discharging cycles were found to deepen the corrosion layer and formation of porous spongy Pb on full discharging. As the number of cycles increased, the amount of PbO formed on discharging of PbO2 --> Pb2+ was found to decrease while PbSO4 increased and the chargeable layer thickness increased.