The dynamical Jahn-Teller effect has been treated in the case of strong coupling for which the static distortional energy of electrons is larger than the energy of a typical vibrational quantum. A perturbation method which applies to strong coupling is developed. The eigenfunction and eigenvalue are expanded as power series of the ratio of the vibrational quantum to the static distortional energy. We have dealt explicitly with the Jahn-Teller effect of the Г8 state of an Oh point group; the energy levels of electronic-vibration system are obtained. The characteristics of strong coupling as compared with weak coupling are: 1) although no static distortion actually appears, the degeneracy and frequency spectra of vibrational modes are changed; 2) the collective modes of electronic-vibration system will appear, if the vibrational modes coupled to the electrons are "tuned". The theory is employed to interpret the experimental results obtained by Weinstock et al. on TcF6 and ReF6 from the infra-red and Raman spectra.