Eg5/KSP is a homotetrameric, Kinesin-5 family member whose ability to cross-link microtubules has associated it with mitotic spindle assembly and dynamics for chromosome segregation. Transient-state kinetic methodologies have been used to dissect the mechanochemical cycle of a dimeric motor, Eg5-513, to better understand the cooperative interactions that modulate processive stepping. Microtubule association, ADP release, and ATP binding are all fast steps in the pathway. However, the acid-quench analysis of the kinetics of ATP hydrolysis with substrate in excess of motor was unable to resolve a burst of product formation during the first turnover event. In addition, the kinetics of P(i) release and ATP-promoted microtubule-Eg5 dissociation were observed to be no faster than the rate of ATP hydrolysis. In combination the data suggest that dimeric Eg5 is the first kinesin motor identified to have a rate-limiting ATP hydrolysis step. Furthermore, several lines of evidence implicate alternating-site catalysis as the molecular mechanism underlying dimeric Eg5 processivity. Both mantATP binding and mantADP release transients are biphasic. Analysis of ATP hydrolysis through single turnover assays indicates a surprising substrate concentration dependence, where the observed rate is reduced by half when substrate concentration is sufficiently high to require both motor domains of the dimer to participate in the reaction.