We present measurements of the energy and angular distributions of energetic protons and alpha particles (>30 keV/charge) in the geomagnetic tail. The measuremnts were made during the recovery phase of a geomagnetic substorm on April 19, 1978, with the Max-Planck-Institut/University of Maryland sensor system on the Isee 1 satellite. The measurements were also correlated with plasma observations made by the LASL/MPE instrument on Isee 1. The data reveal the presence of a thin nonthermal layer of protons and alpha particles at the plasma sheet boundary. The particles have their maximum flux at ~60 keV/charge and are streaming highly collimated in the earthward direction. The alpha particle layer is confined within the proton layer. Many aspects of the observations are in agreement with an acceleration model near the neutral line proposed by Jaeger and Speiser (1974).