Results are presented of calculations of the motion of electrons in slow, large-amplitude fluctuations of the electric field, which have been observed by means of the Swedish satellite Viking. The E∥ component seen by the ionospheric electrons, entering the acceleration region from below, is assumed to vary along the path of the electrons along the magnetic field lines in the way that Viking recorded along its more or less horizontal path through, or above, the accleration region. Although this is a simplified model it is expected to illustrate the effect of the E∥ fluctuations on the ''cold'' electrons, which enter the acceleration region more realistically than in the earlier, highly simplified model used by Hultqvist (1988). The results of the calculations show that temporal variations of E∥ of the kind observed by Viking easily can bring the electrons to the top of an acceleration region, which extends 1000--10,000 km along the magnetic field lines, with energies in the range 100 eV to several keV, as have been observed. ¿American Geophysical Union 1991