This article presents theoretical investigations on techniques for the improvement of the dynamic characteristics of slender bridges under wind action. Aerodynamically effective control shields are applied as controlled actuators. The first part of the article describes the modelling of the uncontrolled aeroelastic system. Acting aerodynamic forces are consistently characterised using linear time-invariant transfer elements in terms of rational functions. On this basis, two configuration levels of the uncontrolled system are represented with linear time-invariant state-space models and investigated. The second part of the article addresses controller design and the behaviour of the controlled aeroelastic system. Both fundamental limits for stabilisation and the efficiency for attenuating the influence of gusts are described for different actuator mechanisms. The results are derived and discussed with methods of control theory.