The tear-strips are formed by transverse cutting of a sheet material by a cutter with a rotary blade, of which the blade cooperates with counter-blades carried by a rotary member. Once formed, each tear-strip is held on the respective counter-blade, for example, by means of a vacuum, so that it can be transferred to a sheet of wrapping material. The tear-strip is applied to the wrapping material transversely by the combined action of the counter-blade and of a striker block carried by a further rotary member disposed on the opposite side of the sheet material. The sheet material can thus advance at a constant speed throughout the process of applying the tear-strips. The preferred use is for automatic packaging machines for products such as food products.