The kinetics of alkali atom transport through intercalation compounds was theoretically considered through numerical simulation of the current transient and concentration profile across the electrode with time. For the theoretical calculation of those two different points of view, the following were considered: that alkali ion diffusion is a rate-controlling step of alkali atom transport through the electrode subjected to ＇real potentiostatic＇ constraint; and that cell-impedance purely governs alkali atom transport. We presented current transient and change in alkali atom content profile across the electrode with time, numerically simulated based upon the two approaches. As an example lithium transport through a carbon-dispersed Li1-deltaCoO2 composite electrode was examined from the two points of view. From the comparison of experimentally obtained current transients with those numerically simulated, it is suggested that lithium transport during intercalation into and deintercalation from the Li1-deltaCoO2 composite electrode in the single alpha phase region are purely governed by cell-impedance. However, the ＇cell-impedance-controlled＇ lithium transport during intercalation into the Li1-deltaCoO2 electrode in the coexistence of two phases alpha and beta is converted into ＇diffusion-controlled＇ lithium transport. This transition in transport mechanism can be accounted for in terms of the input flux at the subsurface toward the electrode between by chemical diffusion and by the quotient of potential drop divided by cell-impedance.