The microscopic origin of the fast dielectric relaxation modes and the integrated dielectric relaxation times of methanol and ethanol was investigated by means of cross-correlation analysis of molecular dynamics simulation. Random force on the fluctuation of collective dipole moment was correlated with the two-body density mode in both real and reciprocal spaces. A strong coupling was observed with the OH alternation mode at 30 nm(-1) suggesting that alternating switching of the hydrogen bond within a hydrogen-bonding chain is the principal origin of the retarded friction on the collective dipole moment. The relaxation of the coupling was much slower than that of the partial intermediate scattering functions at the corresponding wavenumber, which suggests the breakdown of the factorization approximation employed in the mode-coupling theory. Although the prepeak structure is strongly coupled to the viscoelastic relaxation, its coupling with the dielectric relaxation is relatively weak. The difference between the viscoelastic and the dielectric relaxations was discussed in terms of the different symmetries of the shear stress tensor and the collective dipole moment.