  For the one-dimensional nonlinear damped Klein-Gordon equation \[
\partial_{t}^{2}u+2\alpha\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad
\mbox{on $\mathbb{R}\times\mathbb{R}$,}\] with $\alpha>0$ and $p>2$, we prove
that any global finite energy solution either converges to $0$ or behaves
asymptotically as $t\to \infty$ as the sum of $K\geq 1$ decoupled solitary
waves. In the multi-soliton case $K\geq 2$, the solitary waves have alternate
signs and their distances are of order $\log t$.
