The electrostatic pulses observed by satellites in space plasmas are analyzed using the concept of electron phase density holes. The main goal of the study is to clarify the qualitative differences between the actual three-dimensional (3-D) perturbations and the well-known 1-D Bernstein-Greene-Kruskal (BGK) modes of the electron hole type. The 3-D analogues of the BGK holes in magnetoplasmas are discussed in the context of charged-particle dynamics in the localized electrostatic field. It is shown that the anisotropy caused by the geomagnetic field is a decisive factor necessary for the existence of the localized structures observed in the magnetosphere. The possibility of hole-like structures is closely connected with the quasi-one-dimensional nature of the electron motion, predominantly along the external magnetic field. A necessary condition for the existence of the 3-D counterparts of the 1-D BGK holes is deduced.