  We present two types of relativistic Lagrangians for the Lorentz-Dirac
equation written in terms of an arbitrary world-line parameter. One of the
Lagrangians contains an exponential damping function of the proper time and
explicitly depends on the world-line parameter. Another Lagrangian includes
additional cross-terms consisting of auxiliary dynamical variables and does not
depend explicitly on the world-line parameter. We demonstrate that both the
Lagrangians actually yield the Lorentz-Dirac equation with a source-like term.
