Summary: We consider a quasistatic frictionless contact problem for viscoelastic bodies with long memory. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. The adhesion between the contacting surfaces is taken into account and the evolution of the bonding field is described by a first-order differential equation. We derive a variational formulation of the mechanical problem and establish an existence and uniqueness result by using time-dependent variational inequalities, differential equations and the Banach fixed point theorem. Moreover, using compactness properties, we study a regularized problem which has a unique solution and obtain the solution of the original model by passing to the limit as the regularization parameter converges to zero.