Energetic proton and electron dispersion structures are detected at both the dawn and dusk nightside magnetosheath near the equatorial plane using the Geotail Energetic Particles and Ion Composition instrument data. A common feature of all the exhibited examples is that the vector magnetic field progressively scans from northward to southward through all the latitude angles while remaining almost within a plane intersecting the nightside magnetopause. For such geometries, at the duskside magnetosheath, peaks in the energetic electron flux precede those in the proton, whereas the opposite occurs at the dawnside magnetosheath. The peak fluxes of energetic protons (electrons) are measured at the duskside (dawnside) magnetosheath whenever the vector magnetic field points toward the central dusk (dawn) low-latitude boundary layer (LLBL) region of the magnetosphere. Therefore we infer that the energetic electron (proton) source is essentially spatially limited to the central dawn (dusk) LLBL. We interpret the observed dispersion structures as spatial phenomena: Energetic electrons (protons) leak out from-the equatorial dawn (dusk) LLBL and then are channeled along the draped magnetic field lines over the magnetopause toward spacecraft on the duckside (dawnside). The energetic electrons (protons) are detected in the duskside (dawnside) magnetosheath for a larger range of magnetic field latitude angles. In conclusion, the leakage of energetic particles through the magnetopause seems to be a process of great importance, in parallel with the merging one.