  In the last few years, a number of planets have been proposed to orbit
several post main-sequence binary star systems on the basis of observed
variations in the timing of eclipses between the binary components. A common
feature of these planet candidates is that the best-fit orbits are often highly
eccentric, such that the multiple planet systems proposed regularly feature
mutually crossing orbits - a scenario that almost always leads to unstable
planetary systems. In this work, we present the results of dynamical studies of
all multiple-planet systems proposed to orbit these highly evolved binary
stars, finding that most do not stand up to dynamical scrutiny. In one of the
potentially stable cases (the NN Serpentis 2-planet system), we consider the
evolution of the binary star system, and show that it is highly unlikely that
planets could survive from the main sequence to obtain their current orbits -
again casting doubt on the proposed planets. We conclude by considering
alternative explanations for the observed variation in eclipse timings for
these systems.
