This paper proposes a new form of nonsteady-state anti-Stokes near-field spectroscopy with high spatial resolution in Dicke's optical superradiation regime. A system of kinetic equations is constructed that describes collections of excited atoms and fluorescence photons in the far field. It is solved approximately, and a formula is obtained for the signal intensity of nonsteady-state anti-Stokes near-field spectroscopy. Possible ways of constructing a new method of high-spatial-resolution spectroscopy of atoms and molecules are discussed.