There is described a method for applying foil material (200) onto successive sheets (S), especially sheets of securities. In a first step, individual sheets (S) are transported in succession along a sheet transport path. In a second step, at least one continuous band of foil material (200) is applied onto the individual sheets (S) along a direction substantially parallel to a direction of displacement of the individual sheets, thereby forming a continuous flow of sheets linked to one another by the said at least one continuous band of foil material (200). In a third step, the said at least one continuous band of foil material (200) is cut by means of a laser beam such that the continuous flow of sheets is again separated into individual sheets (S) with portions of foil material (200*) remaining on the sheet. The cutting is performed at positions located on the sheets (S) such that said portions of foil material (200*) remaining on the sheets do not extend beyond leading and trailing edges of the sheets (S). Waste portions (205) of said at least one continuous band of foil material (200) that are not to remain on the sheets (S) are evacuated by aspiration, evacuation being carried out by direct aspiration of the waste portions (205) at least at a first position located downstream of and proximate to a cutting position where said at least one continuous band of foil material (200) is cut by the laser beam. There is also described an installation for carrying out the above method.