The invention relates to a method and a device for applying pouring elements (F), which are held by means of a gripping device (6) of an applicator (1) and have a flange and a screw cap, onto packages (P), in particular cardboard/plastic composite packages for flowable products. Each pouring element (F) is supplied to the gripping device (6) in an aligned position, is gripped by gripper jaws (26A, 26B) of a gripper (26) of the gripping device (6), and is applied to a package (P) by the gripping device by means of the pouring element flange and is pressed against the package. The aim of the invention is to achieve a situation-adapted individual pressing of the pouring elements (F) even onto uneven gable surfaces of the packages (P) with a uniformly distributed force in a single pressing process during the application of the pouring elements. This is achieved in that the method according to the invention has the following steps: - gripping a pouring element (F) by closing the gripper jaws (26A, 26B), - lowering each gripping device (6) together with the gripped pouring element (F) onto a package (P) being transported below the pouring element into an application position, - pressing the flange of the pouring element (F) onto the package (P) by means of a pressing head (33) over a specified period, wherein the pressing head (33) can be freely moved in space by a specified angular range and can be adapted to the respective shape of the package gable during the pressing process, and the center of the imaginary adhesive surface remains stationary, and - lifting each gripping device (6) in order to receive a newly supplied pouring element (F).