  Offshell electrodynamics based on a manifestly covariant off-shell
relativistic dynamics of Stueckelberg, Horwitz and Piron, is five-dimensional.
In this paper, we study the problem of radiation reaction of a particle in
motion in this framework. In particular, the case of above-mass-shell is
studied in detail, where the renormalization of the Lorentz force leads to a
system of non-linear differential equations for 3 Lorentz scalars. The system
is then solved numerically, where it is shown that the mass-shell deviation
scalar $\ve$ either smoothly falls down to 0 (this result provides a mechanism
for the mass stability of the off-shell theory), or strongly diverges under
more extreme conditions. In both cases, no runaway motion is observed.
Stability analysis indicates that the system seems to have chaotic behavior in
the divergent case. It is also shown that, although a motion under which the
mass-shell deviation $\ve$ is constant but not-zero, is indeed possible, but,
it is unstable, and eventually it either decays to 0 or diverges.
