We study free electron dynamics during inelastic interaction with the ponderomotive potential of a traveling optical wave using classical and quantum-mechanical models. We show that in the strong interaction regime, the electrons trapped in the periodic potential oscillate leading to periodic revolutions of sharp peaks of the density distributions in the real and momentum spaces. In this regime, the synchronicity between the velocity of the optical wave and the electron propagation velocity is not required. Asynchronous interaction enables acceleration or deceleration of a significant fraction of the electrons to a final spectrum with a relative spectral width of 0.5%-2.5%. This technique allows one to accelerate electrons from rest to keV energies while reaching a narrow spectrum of kinetic energies and femtosecond pulsed operation.