  Relativistic action-at-a-distance theories with interactions that propagate
at the speed of light in vacuum are investigated. We consider the most general
action depending on the velocities and relative positions of the particles. The
Poincare invariant parameters that label successive events along the world
lines can be identified with the proper times of the particles provided that
certain conditions are impossed on the interaction terms in the action. Further
conditions on the interaction terms arise from the requirement that mass be a
scalar. A generic class of theories with interactions that satisfy these
conditions is found. The relativistic equations of motion for these theories
are presented. We obtain exact circular orbits solutions of the relativistic
one-body problem. The exact relativistic one-body Hamiltonian is also derived.
The theory has three components: a linearly rising potential, a Coulomb-like
interaction and a dynamical component to the Poincar\'e invariant mass. At the
quantum level we obtain the generalized Klein-Gordon-Fock equation and the
Dirac equation.
