Power spectral density analysis using Burg's maximum entropy method (MEM) was applied to the geomagnetic dipole field and its rate of change for the years 1901--1969. Both spectra indicate relative maxima at 0.015 cycle/yr and its harmonics. These maxima correspond approximately to 66-, 33-, 22-, 17-, 13-, 11-, and 9-year spectral lines. The application of the same analysis techniques to the length of day (l.o.d.) fluctuations for the period 1865--1961 reveals similar spectral characteristics. the existence of the common spectral peaks with periods of 66 and 33 years in the l.o.d. fluctuations and the geomagnetic dipole field is clearly established. The existence of the higher harmonics with periods of 22, 17, 13, 11, and 9 years is somewhat uncertain because of the line-splitting problem in the MEM spectral analysis. Furthermore, the 22- and 11-year spectral lines cannot be attributed to the solar magnetic cycle and the solar cycle unambiguously because they are the higher harmonics of the 66-year period. We suggest that the spectral line similarity in the l.o.d. fluctuations and the dipole field variations is related to the motion within the earth's fluid core during the past 100 years.