  This paper considers the stability of tidal equilibria for planetary systems
in which stellar rotation provides a significant contribution to the angular
momentum budget. We begin by applying classic stability considerations for two
bodies to planetary systems --- where one mass is much smaller than the other.
The application of these stability criteria to a subset of the Kepler sample
indicates that the majority of the systems are not in a stable equilibrium
state. Motivated by this finding, we generalize the stability calculation to
include the quadrupole moment for the host star. In general, a stable
equilibrium requires that the total system angular momentum exceeds a minimum
value (denoted here as $L_X$) and that the orbital angular momentum of the
planet exceeds a minimum fraction of the total. Most, but not all, of the
observed planetary systems in the sample have enough total angular momentum to
allow an equilibrium state. Even with the generalizations of this paper,
however, most systems have too little orbital angular momentum (relative to the
total) and are not in an equilibrium configuration. Finally, we consider the
time evolution of these planetary systems; the results constrain the tidal
quality factor of the stars and suggest that $10^6\le{Q_\ast}\le10^7$.
