We have obtained high-resolution spectra of 89 M dwarf members of the Pleiades and Hyades and have derived radial velocities, Hα equivalent widths, and spectroscopic rotational velocities for these stars. Typical masses of the newly observed Pleiades and Hyades stars are ∼0.4 M⊙ and ∼0.2 M⊙, respectively. We combine our new observations with previously published data to explore the rotational evolution of young stars with M ≤ 0.4 M⊙. The average rotation rate in the Hyades (age 600 Myr) is about 0.4 times that in the Pleiades (110 Myr), and the mean equivalent widths of Hα 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 ≤ 0.4 M⊙, 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 ≈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.