In the process of deformation of such multilayer structures, significant stresses can arise on the foundation-coating interface because of the difference in their physical and mechanical properties, which can result in fracture or coating separation. The action of static or impact loads on damage onset and development in the adhesive layer in such multilayer structures has been investigated almost completely, but similar processes in the case of suddenly applied vibration loads have not been studied to a large extent. The latter draw attention because of the fact that even small variable actions can localize vibrations near the imperfections (inclusions, defects, etc.) and can be accompanied with an increase in the damage of the adhesion layer, which results in partial separation of the film. In the present paper, the possibility of vibration localization in damaged regions and the influence of the localization on the damage development till the film separation are studied. The first of the possible scenarios of the damage region behavior is its monotone increase. The second scenario of damage behavior is its constant stepwise growth. In this case, damage increases on some time intervals and is constant between the intervals. Under the conditions obtained in the paper, this second scenario can be transformed into the first one. The third scenario is that damage does not increase. This scenario can be realized under sufficiently large vibration load frequencies. Some conditions under which damage behavior is determined by the localized oscillating part of the solution are derived.