In this paper, we propose a theory of adhesive contact of viscoelastic materials in steady state motion. By exploiting a boundary formulation based on Green's function approach, the unknown contact domain is calculated by enforcing a proper local energy balance that takes into account for the contribution of the non-conservative work of internal stresses. The latter is directly related to the odd part of the Green function. The theory predicts that, within a certain a range of velocities, the interaction between adhesion and viscoelasticity leads to enhanced adhesive performance, i.e. larger contact area and pull-off force, compared to the equivalent adhesive elastic case. At low velocity friction is also strongly enhanced compared to the adhesiveless viscoelastic case, mainly as a consequence of adhesion hysteresis induced by the small-scale viscoelasticity. However, at intermediate and high velocity values, the effect of viscoelastic hysteresis occurring at larger scales, i.e. into the bulk, causes friction to increase further. Under these conditions, due to the presence of adhesion, small-scale and bulk contribution to friction cannot be linearly separated. As consequence of the finiteness of the contact length, the energy release rates follow a non-monotonic trend, which is not observed during crack propagation or healing in infinite systems. All the presented results are strongly supported by existing experimental evidences.