A model describing the flat contact with adhesion between rough solid bodies has been set up, in which the set of asperities is described as a third thin body. Due to the local compressive stresses, the cavities close up during compressive loading, leading to increased adhesion in the contact area. An internal variable model describing the evolution of the intensity of adhesion in the contact between the two solids is set up, based on the thermodynamics of irreversible processes. From a perturbation method, a material surface model for the third body is derived. The Hertz theory of the plane contact between solid elastic bodies is then modified in order to account for the increased adhesion when both solids are pressed together. The specific problem of the compression of a rubber hemisphere on a glass plate is analysed. In that situation, the analytical model predicts in a satisfactory way the true area of contact vs. the compressive force. In the second part of the paper, the model is extended to describe the time dependence of adhesion. Predictions of the evolution of the physical area of contact vs. time are demonstrated, in cases of both conformal and non-conformal contact conditions. The relevance of the model is further discussed.