A method of applying an adhesive film to a component includes applying an adhesive film to a surface of a component, wherein the adhesive film is positioned between the surface and an elastic membrane, the elastic membrane is transferred into a curved state with a convex and a concave side and contacted with the surface with the convex side first such that an adhesive layer of the adhesive film is pressed onto the surface in a full-area by the elastic membrane, the adhesive layer is pressed onto the surface in a full-area by a negative pressure being applied to that side of the elastic membrane facing towards the adhesive film, and to stabilize the component against deformation brought about by this negative pressure, the elastic membrane along with the adhesive film is pushed against the surface of the component with a plunger means.