  We discuss a covariant generalization of the parametrized post-Newtonian
(PPN) formalism in a class of scalar-tensor theories of gravity. It includes an
exact construction of a set of global and local (Fermi-like) references frames
for an isolated N-body astronomical system as well as PPN multipolar
decomposition of gravitational field in these frames. We derive PPN equations
of translational and rotational motion of extended bodies taking into account
all gravitational multipoles and analyze the body finite-size effects in
relativistic dynamics that can be important at the latest stages of orbital
evolution of coalescing binary systems. We also reconcile the IAU 2000
resolutions on the general relativistic reference frames in the solar system
with the PPN equations of motion of the solar system bodies used in JPL
ephemerides.
