Time-series spectral analysis has been performed on the dates of geomagnetic reversals of the last 20 Myr BP and earlier. Possible evidence is found from the presence of high spectral peaks for two very long periodicities, 0.4 Myr and 1.3 Myr, that may be associated with slow variations of the Earth's orbital eccentricity as predicted by Berger. However, statistical significance tests and a number of other arguments do not confirm the two detections.