Shear Alfv¿n waves with amplitudes >100 mV/m were observed on two recent sounding rocket flights: one flown from Poker Flat, Alaska, to an altitude of 1040 km in the evening auroral zone, and another flown from Sondre Stromfjord, Greenland, to an altitude of 770 km in the morning cusp region. The largest waveforms are best described as a series of step functions, rather than as broadband noise or as single frequency waves. Complete two-dimensional E and B measurements at 4-ms time resolution wer made, showing a downward propagation direction and implying insignificant reflection from the ionosphere at frequencies greater than 1 Hz. Intense, field-aligned, low-energy electron fluxes accompany the waves. Acceleration of these electrons by the Alfv¿n waves, either through the resonant acceleration mechanism described by Temerin et al. (1986), or through the nonresonant mechanism described by Goertz and Boswell (1979), is shown to be feasible. The waves in at least one case have a sufficiently large ponderomotive potential to generate the observed density fluctuations of order 1. ¿ American Geophysical Union 1990