Manganese oxide/graphite oxide (GO) composites containing GO of two different oxidation levels are investigated as supercapacitors in neutral electrolytes, Na₂SO₄ and Li₂SO₄. Addition of only 10 wt% of GO with a low oxidation level results in an 18 times improvement in the capacitance in lithium sulfate and in a 60 times improvement of the capacitance in sodium sulfate as compared to that measured on manganese oxide. Even though the performance of the composites is similar in both electrolytes, in Na₂SO₄ the electrodes are more stable and the capacitance retention ratio is higher. The charge storage in sodium sulfate is linked to the double layer capacitance in the small pores of the composites and to the pseudocapacitance of the manganese oxide phase. In lithium sulfate the insertion of the lithium cation into the structure of the manganese oxide phase enhances the performance. Addition of GO with a high oxidation level is not favorable owing to the defects in the graphene layers limiting the conductivity and charge propagation for Faradaic reactions.