  We generalize electrodynamics with a second interaction in lightcone. The
time-reversible equations for two-body motion define a semiflow on
$C^2(\mathbb{R})$ with four state-dependent delays of neutral type and
nonlinear gyroscopic terms. Furthermore, if the initial segment includes
velocity discontinuities, their propagation requires two energetic corner
conditions defining boundary layer neighborhoods of large velocities and small
denominators. Finally, we discuss a motion restricted to a straight line and a
segment pair with vanishing accelerations that iterates to another
constant-velocity segment pair.
