A theoretical analysis is performed for the study of the bonding of a viscoelastic rough surface to a rigid substrate. The mechanics of contact and adhesion are studied with the Dugdale–Barenblatt model for surface interaction. Exact solutions are obtained for arbitrary surface profiles and loading histories. Detailed solutions are given for a power-law viscoelastic material. This solution is used to determine the time for the self-bonding of surfaces (solid sintering under zero load). The time to self-bonding is shown to be extremely sensitive to the aspect ratio of the asperities. A closed form expression is derived for the time needed to achieve full contact when the surfaces are compressed with a load that increases linearly with time. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 545–561, 2002; DOI 10.1002/polb.10113