  The equations of motion of compact binary systems have been derived in the
post-Newtonian (PN) approximation of general relativity. The current level of
accuracy is 3.5PN order. The conservative part of the equations of motion
(neglecting the radiation reaction damping terms) is deducible from a
generalized Lagrangian in harmonic coordinates, or equivalently from an
ordinary Hamiltonian in ADM coordinates. As an application we investigate the
problem of the dynamical stability of circular binary orbits against
gravitational perturbations up to the 3PN order. We find that there is no
innermost stable circular orbit or ISCO at the 3PN order for equal masses.
