The origin of the main geomagnetic field is related to the current in the fluid core of Earth. A close relationship between the fluctuations of the rotation of Earth and the secular changes of the geomagnetic field is suspected. Two-channel maximum entropy spectral analyses are applied to the dipole moments of Earth from 1901 to 1980 and the rotational rate fluctuations from 1890 to 1987 in this study. The common spectral peaks are found with periods of 51, 34, 22, 13, and 9.5 years. The values of the coherence are above 0.99, 0.98, 0.95, 0.95, and 0.77 at these peaks. The 51- and 34-year spectral peaks are the dominant ones. The time lags of the magnetic field are 3.1¿0.6 years and 22.4¿4.5 years, respectively. Two simulated time series are constructed with the obtained time lags. They exhibit features similar to the actual time series of the dipole moment variations and Earth's rotational fluctuations. ¿ American Geophysical Union 1992