  Surface roughness is known to easily suppress the adhesion of elastic
surfaces. Here a simple model for the contact of \emph{viscoelastic} rough
surfaces with significant levels of adhesion is presented. This approach is
derived from our previous model [E. Barthel and G. Haiat {\em Langmuir}, 18
9362 2002] for the adhesive contact of viscoelastic spheres. For simplicity a
simple loading/unloading history (infinitely fast loading and constant pull-out
velocity) is assumed. The model provides approximate analytical expressions for
the asperity response and exhibits the full viscoelastic adhesive contact
phenomenology such as stress relaxation inside the contact zone and creep at
the contact edges. Combining this model with a Greenwood-Williamson statistical
modeling of rough surfaces, we propose a quantitative assessment of the
adhesion to rough viscoelastic surfaces. We show that moderate viscoelasticity
efficiently restores adhesion on rough surfaces over a wide dynamic range.
