We recently reported the first pump-probe measurements on the hydrated electron with sufficient time resolution (similar to 35 fs) to directly observe the initial processes in the solvation dynamics of this key prototype for condensed-phase dynamics [Silva, C,; Walhout, P. K.; Yokoyama, K.; Barbara, P. F, Phys. Rev. Lett. 1998, 80, 1086]. An unprecedented relaxation process for the hydrated electron was observed that occurs on the 35-80 fs time scale and exhibits a solvent isotope effect (tau(D2O)/tau(H2O) similar to 1.4), The new process was assigned to inertial/librational motion of the water surrounding the excess electron. The present paper reports a more extensive study of the similar to 35 fs resolved dynamics of the hydrated electron in H2O and D2O at more probe wavelengths and as a function of pump-pulse intensity. The results are in agreement with the preliminary report and support the importance of librational water motion in the relaxation dynamics of the hydrated electron. New high excitation pulse intensity measurements reveal evidence of a high-intensity, two-photon channel involving ejection of the hydrated electron from its initial site to a different site in the solvent.