The change of intensities of optical transitions of atoms, molecules, and their ions in the near field of nanoobjects is of interest for researchers from both basic and applied points of view. The concept of a near field was used as early as the 1960s to study the mechanisms of hypersensitive transitions of rare-earth (RE) ions. In this work, it is once more emphasized that, precisely for these transitions, changes in characteristics under the action of local properties of the medium are especially strong and, correspondingly, these transitions are especially promising for use. The Judd method for the calculation of the intensities of hypersensitive transitions of RE ions taking into account the inhomogeneous ligand field is extended to RE ions in the near field of nanoobjects. A simple analytical expression for the Judd-Ofelt intensity parameter Omega(2) for RE ions in the field of spherical nanoparticles of a subwavelength size is derived.