Electrochemical impedance spectroscopy (EIS) was used to study the kinetics and insertion mechanism of alkali metals in single wall carbon nanotubes (SWNT). Three distinct processes with very different time constants were identified: charge transfer across the macroscopic electrolyte/electrode interface, diffusion through the mesoscale porosity of the SWNT electrode, and nanoscale diffusion in individual SWNT ropes. Electrode resistance and capacitance from EIS compare well with direct dc measurements. We propose that alkalis decorate the internal and external surfaces of the SWNT ropes.