The nanotip of a needle used in apertureless optical scanning microscopy is modeled by a prolate nanospheroid, possessing resonance properties due to the plasmons excited therein. The influence of the resonant nanospheroid on a dipole decay rate of an excited molecule is considered, The relationship between the scanning signal and the molecule position and its dipole momentum orientation is found. The results predict the about one nanometer spatial resolution of some versions of SNOM. (C) 2002 Published by Elsevier Science B.V.