  In a purely Keplerian picture, the anomalistic, draconitic and sidereal
orbital periods of a test particle orbiting a massive body coincide with each
other. Such a degeneracy is removed when a post-Keplerian perturbing
acceleration enters the equations of motion yielding generally different
corrections to the Keplerian period for the three aforementioned characteristic
orbital timescales. They are analytically worked out in the case of the
accelerations induced by the general relativistic post-Newtonian
gravitoelectromagnetic fields and, to the Newtonian level, by the oblateness of
the central body as well. The resulting expressions hold for completely general
orbital configurations and spatial orientations of the spin axis of the
primary. Astronomical systems characterized by extremely accurate measurements
of the orbital periods like, e.g., transiting exoplanets and binary pulsars,
may offer potentially viable scenarios for measuring such post--Keplerian
features of motion, at least in principle. As an example, the sidereal period
of the brown dwarf WD1032 + 011 b is currently known with an uncertainty as
small as $\simeq 10^{-5}\,\mathrm{s}$, while its predicted post-Newtonian
gravitoelectric correction amounts to $0.07\,\mathrm{s}$; however, the accuracy
with which the Keplerian period can be calculated is just 572 s. For the double
pulsar PSR J0737-3039, the largest relativistic correction to the anomalistic
period amounts to a few tenths of a second, given a measurement error of such a
characteristic orbital timescale as small as $\simeq 10^{-6}\,\mathrm{s}$. On
the other hand, the Keplerian term can be currently calculated just to a
$\simeq 9$ s accuracy. In principle, measuring at least two of the three
characteristic orbital periods for the same system independently would allow to
cancel out their common Keplerian component provided that their difference is
taken.
