The lithium-excess manganese oxides are a candidate cathode material for the next generation of Li-ion batteries because of their ability to reversibly intercalate more Li than traditional cathode materials. Although reversible oxidation of lattice oxygen has been proposed as the origin of this anomalous excess capacity, questions about the underlying electrochemical reaction mechanisms remain unresolved. Here, we critically analyse the O2−/O− oxygen redox hypothesis and explore alternative explanations for the origin of the anomalous capacity, including the formation of peroxide ions or trapped oxygen molecules and the oxidation of Mn. First-principles calculations motivated by the Li–Mn–O phase diagram show that the electrochemical behaviour of the Li-excess manganese oxides is thermodynamically consistent with the oxidation of Mn from the +4 oxidation state to the +7 oxidation state and the concomitant migration of Mn from octahedral sites to tetrahedral sites. It is shown that the Mn oxidation hypothesis can explain the poorly understood electrochemical behaviour of Li-excess materials, including the activation step, the voltage hysteresis and voltage fade.