Add to ORKGWe sum up the next-to-leading logarithmic corrections to the heavy-quarkonium hyperfine splitting using the nonrelativistic renormalization group. On the basis of this result, we predict the mass of the #eta#_b meson to be M(#eta#_b)=9421#+-#10 (th)_-_8"+"9 (#delta##alpha#_s) MeV. The experimental measurement of M(#eta#_b) with a few MeV error would be sufficient to determine #alpha#_s(M_Z) with an accuracy of #+-#0.003. The use of the nonrelativistic renormalization group is mandatory to reproduce the experimental value of the hyperfine splitting in charmonium. (orig.)SIGLEAvailable from TIB Hannover: RA 2999(03-172) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman