  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 center of mass is rather a center of energy.
Individual energies are separately conserved and the meaning of their
positivity is discussed in terms of world-lines. Several results derived
decades ago under restrictive assumptions are extended to the general case.
Relative motion has a structure similar to that of a nonrelativistic one-body
motion in a stationnary external potential, but its evolution parameter is
generally not a linear function of the center-of-mass time, unless the relative
motion is circular (in this latter case the motion is periodic in the
center-of-mass time). Finally the case of an extreme mass ratio is
investigated. When this ratio tends to zero the heavy body coincides with the
center of mass provided that a certain first integral, related to the binding
energy is not too large.
