Electrochemical synthesis of graphene oxide (GO) is known to occur with potential oscillations, but the structural changes underlying these oscillations have remained unclear. In situ time-resolved synchrotron radiation X-ray diffraction demonstrates that the electrochemical synthesis of GO in aqueous H2SO4 can be described as an oscillating reaction. The transformation from graphite to GO proceeds through periodic structural oscillations that correlate with potential cycles. Stage-1 graphite intercalation compound (GIC) is found only at the peak of the potential cycle, but not at the bottom of the cycle. Stage-1 GIC is formed in the first half-cycle from stage-2 GIC and then transforms into "pristine graphite oxide" (PGO) on the lower side of the potential cycle, after which the cycle restarts with the formation of a new portion of stage-1 GIC. Water-washing results in the transformation of PGO into water-swollen GO with d(001) ~11 Å. These periodic structural changes can be considered a new type of oscillating reaction. The presented results provide broad insights into the oscillating structural changes occurring during the anodic graphite oxidation in aqueous H2SO4 and allow to update of the mechanism of GO electrochemical formation.