Three closely related models for two-layered beams in which slip can occur at the interface are described. In the first, beam layers are modelled under the assumptions of Timoshenko beam theory. Along the interface, an adhesive layer of negligible thickness bonds the surfaces so that a small amount of slip is possible. Friction is assumed to be proportional to the rate of slip. The second is obtained from the first by letting the shear stiffness of each beam tend to infinity. The third is obtained from the second by assuming that the moment of inertia parameter is negligible. In the last case, an analog of the Euler–Bernoulli beam is obtained which exhibits frequency proportional damping characteristics. The three models are compared, both numerically and analytically, and found to be in close agreement for low frequency motions. Optimal damping rates are calculated for these low frequency motions.