The problems of construction of the generalized Poincaré-invariant equations of
motion of the nonpoint objects are discussed. A short outline of revived methods of an
action-at-a-distance description of interacting particles is given. A new approach to
the problem of motion in relativistic gravity is discussed. The generalized Poincaréinvariant equations of motion are derived in post-Newtonian approximations of the phenomenological formulation of the relativistic action-at-a-distance gravity.