Precessing elliptical motion (PEM) is an important possible trajectory of the virtual geomagnetic pole (VGP), and expected result of the superposition of dipole precession on nondipole elliptical motion as proposed and reported on in the literature. The complex plane spectral signature of a simple PEM combination is shown here to be bichromatic in general, consisting of two peaks at frequencies ωa and ωb. Associated with these two peaks is a frequency pair (-ω0, ω0) from which each of the peaks at ωa and ωb is shifted by an amount ωp. This shift corresponds to the frequency of precession of the axis of the elliptical motion modified by the precession. Shifts towards positive (negative) frequencies correspond to counterclockwise (clockwise) precessions. The complex plane spectrum associated with a PEM can be strongly asymmetrical and does not provide the investigator with a straightforward means of extracting the frequencies of the component precessional and elliptical motions which may belie processes fundamental to the geomagnetic field. To overcome this problem, an enhanced complex plane spectral analysis is developed which directly identifies both the frequencies of the component precessional and elliptical motions. Examples of the application of this method are given using discretely sampled, synthetic VGP time series. ¿ American Geophysical Union 1993