  The distinction between the mean anomaly $\mathcal{M}(t)$ and the mean
anomaly at epoch $\eta$, and the mean longitude $l(t)$ and the mean longitude
at epoch $\epsilon$ is clarified in the context of a possible use of such
orbital elements in post-Keplerian tests of gravity, both Newtonian and
post-Newtonian. In particular, the perturbations induced on
$\mathcal{M}(t),\,\eta,\,l(t),\,\epsilon$ by the post-Newtonian Schwarzschild
and Lense-Thirring fields, and the classical accelerations due to the
atmospheric drag and the oblateness $J_2$ of the central body are calculated
for an arbitrary orbital configuration of the test particle and a general
orientation of the primary's spin axis $\boldsymbol{\hat{S}}$. They provide us
with further observables which could be fruitfully used, e.g., in better
characterizing astrophysical binary systems and in more accurate
satellite-based tests around major bodies of the Solar System. Some erroneous
and misleading claims by Ciufolini and Pavlis appeared in the literature are
confuted. In particular, it is shown that there are no net perturbations of the
Lense-Thirring acceleration on either the semimajor axis $a$ and the mean
motion $n_\mathrm{b}$. Furthermore, the quadratic signatures on
$\mathcal{M}(t)$ and $l(t)$ due to certain disturbing non-gravitational
accelerations like the atmospheric drag can be effectively disentangled from
the post-Newtonian linear trends of interest provided that a sufficiently
extended temporal interval for the data analysis is assumed. A possible use of
$\eta$ along with the longitudes of the ascending node $\Omega$ in tests of
general relativity with the existing LAGEOS and LAGEOS II satellites is
suggested.
