In this paper, transverse vibration control and transport velocity control of a moving web in a rewinding section of a roll to roll system are investigated. The moving web is modeled as an axially moving beam. Two independent adaptive control schemes are proposed. The first control scheme using a control force exerted from a hydraulic actuator is to suppress transverse vibrations of the moving web of unknown mass per unit length under a spatially varying tension and a time-varying transport velocity. The second control scheme using a control torque applied to the rewind roller is to maintain the transport velocity levels of the moving web in spite of disturbances such as the variations of rotating elements and unknown bearing friction. From the decentralized control viewpoint, the uniformly exponential stability for suppressing the transverse vibrations and the uniformly asymptotic stability for maintaining the transport velocity are achieved. However, as a whole, the uniformly asymptotic stability is concluded. Simulations for demonstrating the effectiveness of the proposed control schemes are presented.