Observations made with the electron spectrometer on the ISEE 1 spacecraft have been used to perform a study of the electron distribution function in the low-latitude boundary layer of the magnetosphere (LLBL) in the sunward direction. The LLBL is defined to be a layer of plasma of thickness ~RE inside and adjacent to the magnetopause, having a density intermediate between that of the magnetosheath and the magnetosphere. The study included 43 examples of especially well defined layers having densities, nBL, such that (nmagnetosphere/nBL)~0.1 and (nBL/nmagnetosheath)~0.3, although both ratios were occasionally as low as 0.01. Recent observations (e.g., Burch et al., 1983) have indicated that electrons with energies in the 100 eV range are frequently exchanged between the ionosphere and the magnetosphere, traveling along the magnetic field lines near to the cusps and giving rise to Birkeland currents. Using three-dimensional model-independent distribution functions of electrons observed in the boundary layer, we have identified beams of field aligned electrons with energy maximum typically 100 eV, distributed over the energy range 50 eV to 200 eV, streaming in either one or both directions. The phase densities in the LLBL and at lower altitudes are similar, and assuming no further acceleration to have occurred, we identify the beams we observe in the LLBL with those observed at lower altitudes. They form an important component of the plasma electrons in the LLBL, which otherwise resembles a mixture of magnetosheathlike and magnetospheric electrons. The bidirectional streaming also suggests that the field lines threading the LLBL are often closed. The reduced distribution functions of electrons in the LLBL do not show positive slopes in the velocity range of the beams, suggesting that the plasma is stable to the growth of longitudinal electrostatic waves.