The authors consider a one-dimensional time-dependent nonlinear system of two partial differential equations
where , , and . Such a system can represent a one-dimensional nonlinear string-beam system describing the vertical oscillations of a suspension bridge which is coupled with the main cable by the stays. The main cable is modelled as a vibrating string and the roadbed of the bridge is represented by a bending beam with simply supported ends. Using Faedo-Galerkin method combined with a semigroup approach, the authors prove the existence of an absorbing set for the solution of the system. Moreover, the existence of a global attractor of the semigroup associated with the system is obtained.