  We construct a supersymmetrized version of the model to the radiation damping
\cite{03} introduced by the present authors \cite{ACWF}. We dicuss its
symmetries and the corresponding conserved Noether charges. It is shown this
supersymmetric version provides a supersymmetric generalization of the Galilei
algebra obtained in \cite{ACWF}. We have shown that the supersymmetric action
can be splited into dynamically independent external and internal sectors.
