Abstract <p>The theory of the ponderomotive forces in space plasma represents an essential part of the solar-terrestrial physics. The problem that appears when the classical expression governing the ponderomotive force is used for analysis of ion acceleration in the Earth’s magnetosphere under the influence of the ion-cyclotron wave is described. It consists in the fact that the force tends to infinity when the wave frequency approaches the local ion gyrofrequency. It is demonstrated that the singularity appears due to idealizations unavoidably adopted upon construction of the standard theory of ponderomotive forces. Two limiting cases are analyzed: the case of a wide opacity band for the ion-cyclotron waves and the case of narrow opacity band. Two approaches for regularization of the ponderomotive force in the vicinity of the pole of the refractive index for the ion-cyclotron wave are proposed. One of them removes the singularity at the pole at the boundary of the wide opacity band while the other removes it at the boundary of the narrow opacity band. Examples of situations in which the singularity in the ponderomotive force calculated within the framework of the standard theory has to be taken into account when studying wave phenomena in the near-Earth plasma are pointed out.</p>