The lithium insertion and extraction dynamics of spinel LiMn2O4/carbon composite electrodes used in lithium-ion batteries have been investigated. A numerical model has been developed which rationalizes these electrodes as a bed of spherical Li1-delta Mn2O4 particles (0 less than or equal to delta less than or equal to 1, depending on the degree of insertion) with carbon as an electrically conducting additive, and with electrolyte filling the pores. It can be concluded from the simulations of potential step (PS) experiments that solid-state diffusion of lithium ions in the Li1-delta Mn2O4 particles and the electrochemical reaction at the Li1-delta Mn2O4 particle surfaces are simultaneously rate-determining. Their relative importance depends on the applied overpotential. Further, the diameter of the primary particles rather than that of the primary particle agglomerates was found to be relevant for the dynamics. From the simulations, we could evaluate a value of 2.8 x 10(-13) cm(2)/s for the solid-state diffusion coefficient of lithium in Li1-delta Mn2O4 particles, a value of 5.5 x 10(-8) cm/s for the standard heterogeneous rate constant, and a value of 0.30 for the transfer coefficient a.