Sustained voltammetric responses, with periods 2-12 times longer than the period of the cycling potential, were found in application of cyclic voltammetry to the oxidation of methanol at a rotating platinum disk in alkaline solution. Experiments were conducted in which a control parameter (the upper potential limit of the potential cycle) was varied. The results demonstrate that the periodic states are ordered in the same way as dynamical states with the same symbolic representations are ordered in a combined forward and reverse U-sequence. Between ranges of the bifurcation parameter for which periodic states were observed, aperiodic behavior was found that possessed properties that are characteristic of deterministic chaos. High-order periodic responses were also obtained in experiments in which the system was allowed to relax under fixed conditions following the transfer of the Pt electrode to the methanol solution. These results provide evidence that the high-order periodic states do not arise from a slow aging process but, instead, are a consequence of the electrochemical mechanism for the voltammetric oxidation of methanol.