The addition of double-layer capacitance into a mathematical model of a dual lithium ion insertion cell is investigated. Double-layer capacitance is introduced in both the negative electrode and the positive electrode. For the purposes of this paper, a LixC6{propylene carbonate +1 M LiClO4}LiyMn2O4 cell is used for the collection of simulation results. Simulation results on the effect of short-time purses passed through the cell are presented. Differences in the transient potential response in the negative and positive electrodes at short times are compared in cells with and without double-layer capacitance using both linear and Butler-Volmer kinetics. Comparisons are made between an electrode with a resistive film and one without and between situations with small and large rates of change of the open-circuit potential with state of charge. A simpler resistive-capacitive model is developed which clarifies many features of the modified behavior due to the capacitance but without simultaneously dealing with the discharge of the active material and concentration gradients.