  In Minkowski spacetime, we consider an isolated system made of two pointlike
bodies interacting at a distance, in the nonradiative approximation. Our
framework is the covariant and a priori Hamiltonian formalism of "predictive
relativistic mechanics", founded on the equal-time condition. The issue of an
equivalent one-body description is discussed. We distinguish two different
concepts: on the one hand an almost purely kinematic relative particle, on the
other hand an effective particle which involves an explicit dynamical
formulation; several versions of the latter are possible. Relative and
effective particles have the same orbit, but may differ by their schedules.
