Adaptive　vibration　control　is　investigated　for　axially　moving　strings　with　a　tensioner.　The　tensioner　is　treated　as　an　actuator.　The　Lyapunov　analysis　is　employed　to　design　a　control　law　that　asymptotically　stabilizes　the　string.　The　proposed　controller　can　estimate　the　parameters　online.　The　Lyapunov　stability　guarantees　the　convergence　of　the　transverse　vibration　of　the　controlled　span　of　the　string　as　well　as　the　estimation　error　of　the　unknown　parameters　to　zero.　The　proposed　controller　is　numerically　tested　for　the　string　under　initial　and　external　disturbances.　Simulation　results　demonstrate　the　effectiveness　of　the　controller.　(C)　2006　Published　by　Elsevier　Ltd.