This thesis considers the dynamics of a viscoelastic Link model. Though the constitutive equation is linear, the problem has a geometrical nonlinearity and an imperfection. This work extends and formalises that done by Hunt and Thompson, which studies the elastic model, and that of Hayman, which studies the quasi-static approximation to the viscoelastic model. The non-linear, dynamic elastic and viscoelastic Link problems and the quasi-static approximation to the latter are rigorously analysed. The equilibria and their stability and bifurcation properties are determined and compared for the perfect and imperfect models. In particular, it is shown that the quasi-static approximation indicates stability at some equilibrium points, corresponding to large deflection, where the dynamic analysis indicates that the system is unstable. Asymptotic approximations to the solution of the linearised problem, subject to different loading strategies, are calculated using multiple scale methods.