Comparisons of the arrivals and disappearances of plasma sheet electrons observed by the Los Alamos Scientific Laboratory/Max-Planck-Institut analyzers on board the Isee 1 and 2 satellites during the course of a magnetic substorm often show relative time delays between the two satellites on the order of a few seconds. Time decay measurements have been used to determine the motion of the northern plasma sheet boundary during substorms for the period February 5 to May 25, 1978. Near substorm onset the average velocity of the surface of the plasma sheet is 23¿18 km/s toward the center of the sheet. And for the same times the average component of the plasma flow based upon moment integrations of the proton distribution is 20¿8 km/s in the same direction. During substorm recovery the plasma sheet reappears, its surface moving outward from the center with an average velocity of 133¿31 km/s as determined by timing its arrival at the two satellites. However, the corresponding proton flow speed is only 3¿7 km/s. At the time of the recovery precursory appearances of the plasma sheet often occur. The time delays associated with these precursors imply that the surface of the plasma sheet moves both upwards and downwards with speeds ~100 km/s. Both the appearance of the precursors and the large difference between the velocity of the plasma sheet surface and the velocity of the flow normal to the surface can be explained by the occurrence of surface waves at the boundary of the plasma sheet which propagate past the satellites at a velocity of 200--600 km/s in the direction of the convective flow. Estimating the tilt of the wave surfaces as ¿15 ¿, we deduce an average wavelength of 1--5 RE and a wave amplitude of ~600--1400 km. Taking into consideration the wave structure at the time of a recovery, we compute a velocity of ~30 km/s for the net outward motion of the plasma sheet boundaries during substorm recovery.