  Using chiral perturbation theory we calculate the imaginary parts of the $K_L
\rightarrow \pi^+ \pi^- e^+ e^-$ form factors that arise from $\pi \pi
\rightarrow \pi^+ \pi^-$ and $\pi \pi \rightarrow \pi^+ \pi^- \gamma^*$
rescattering. We discuss their influence on CP violating variables in $K_L
\rightarrow \pi^+ \pi^- e^+ e^-$.
