  The kinetics of irreversible annihilation of charged particles performing
overdamped motion induced by long-range interaction force, $F(r)\sim
r^{-\lambda}$, is investigated. The system exhibits rich kinetic behaviors
depending on the force exponent $\lambda$. In one dimension we find that the
densities decay as $t^{-1/(2+\lambda)}$ and $t^{-1/(1+2\lambda)}$ when
$\lambda>1$ and $1/2<\lambda<1$, respectively, with logarithmic correction at
$\lambda=1$. For $\lambda \leq 1/2$, the asymptotic behavior is shown to be
dependent on system size.
