We represent a detailed analysis of a series of five successive upstream proton events observed within a 1-hour time period on October 11, 1978. The observations were made by the low-energy proton instrument on ISEE 3, which is designed to measure three-dimensionsal anisotropies in the energy range 35--1600 keV. We have selected this particular series of events from the large number of upstream proton events observed at the position of ISEE 3, more than 200 RE upstream from the earth's bow shock, because the magnetic field at the time was quiet and the characteristics of the propagation of upstream protons were unusually clear. We examine in detail the intensity profiles and properties of the anisotropies. Of particular interest are effects in the anisotropy direction as the spacecraft enters or leaves a particle-population region. Analysis of the directions of the gradient anisotropies at the onsets and ends of the events reveals that upstream protons propagate in sheets or slabs from the earth's bow shock out to ISEE 3.