  In a two-planet system, due to Sundman (1912) inequality, a topological
boundary can forbid close encounters between the two planets for infinite time.
A system is said Hill stable if it verifies this topological condition. Hill
stability is widely used in the study of extra solar planets dynamics. However
people often use the coplanar and circular orbits approximation.
  In this paper, we explain how the Hill stability can be understood in the
framework of Angular Momentum Deficit (AMD). In the secular approximation, the
AMD allows to discriminate between a priori stable systems and systems for
which a more in depth dynamical analysis is required. We show that the general
Hill stability criterion can be expressed as a function of only the semi major
axes, the masses and the total AMD of the system. The proposed criterion is
only expanded in the planets-to-star mass ratio $\epsilon$ and not in the
semi-major axis ratio, in eccentricities nor in the mutual inclination.
Moreover the expansion in $\epsilon$ remains excellent up to values of about
$10^{-3}$ even for two planets with very different mass values.
  We performed numerical simulations in order to highlight the sharp change of
behaviour between Hill stable and Hill unstable systems. We show that Hill
stable systems tend to be very regular whereas Hill unstable ones often lead to
rapid planet collisions. We also remind that Hill stability does not protect
from the ejection of the outer planet.
