  In this paper, a nonlinear axially moving string with the Kelvin-Voigt
damping is considered. It is proved that the string is stable, i.e., its
transversal displacement converges to zero when the axial speed of the string
is less than a certain critical value. The proof is established by showing that
a Lyapunov function corresponding to the string decays to zero exponentially.
It is also shown that the string displacement is bounded when a bounded
distributed force is applied to it transversally. Furthermore, a few open
problems regarding the stability and stabilization of strings with the
Kelvin-Voigt damping are stated.
