A simple asperity model using random process theory is developed in the presence of adhesion, using the Derjaguin, Muller and Toporov model for each individual asperity. A new adhesion parameter is found, which perhaps improves the previous parameter proposed by Fuller and Tabor which assumed identical asperities - the model in all his variants for the radius always gives a finite pull-off force, as in Fuller and Tabor, and contrary to the exponential asperity height distribution, where the force is either always compressive, or always tensile. It is shown that a model with spheres having a radius only dependent on height is a reasonable approximation with respect to models having also a distribution of radius curvatures - the three models differ considerably, as opposed to the adhesionless case where these details did not matter. The important surface parameters in the theory determining the pull-off force are the three moments m(0), m(2), m(4). The asymptotic form of the model at large separation is solved in closed form. As the theoretical pull-off of aligned asperities having the same radius (the average value) increases with the square root of the Nayak bandwidth of the roughness, and as asperity models are known to describe less well the surface at large bandwidth parameters, the limit behavior at large bandwidths remains uncertain.