The count rates of 1.5- and 6-keV electrons measured on ISEE 1 and ISSE 2 are at times strongly spin modulated despite the fact that the axes of the detectors lie along the spin axis of the spacecraft. Spatial gradients in the guiding center density are ruled out as a cause of the spin modulation. The characteristics of the spin modulation can be explained if the electron velocity distribution is nongyrotropic. The procedure is to show that the direction of the plasma flow velocity during times of spin modulation does not lie along the direction of the local magnetic field when both are projected onto the ecliptic plane. While a gyrotropic distribution will cause spin modulation, the count rate maximum will correspond to the direction of the local magnetic field. Gyrophase-bunched electrons are seen within a few tens of kilometers of the shock and as far upstream as 30,000 km from the shock, suggesting that a wave is associated with their propagation. The magnetosheath electrons in the same energy range are also nongyrotropic at times.