We have obtained high-resolution spectra of 89 M dwarf members of the Pleiades and Hyades and have derived radial velocities , H \alpha equivalent widths , and spectroscopic rotational velocities for these stars . Typical masses of the newly-observed Pleiades and Hyades stars are \sim 0.4 M _ { \sun } and \sim 0.2 M _ { \sun } , respectively . We combine our new observations with previously published data to explore the rotational evolution of young stars with M \leq 0.4 M _ { \sun } . The average rotation rate in the Hyades ( age 600 Myr ) is about 0.4 that of the Pleiades ( 110 Myr ) , and the mean equivalent widths of H \alpha are also lower . As found in previous studies , the correlation between rotation and chromospheric activity is identical in both clusters , implying that the lower activity in the Hyades is a result of the lower rotation rates . We show that a simple scaling of the Pleiades rotational distribution for M \leq 0.4 M _ { \sun } , corrected for the effects of structural evolution , matches that of the Hyades if the average angular momentum loss from the Pleiades to the Hyades age is factor of \approx 6 . This suggests that the distribution of initial angular momenta and disk-locking lifetimes for the lowest mass stars was similar in both clusters . We argue that this result provides further evidence for a saturation of the angular momentum loss rate at high rotational velocities .