PCT No. PCT/IB97/00641 Sec. 371 Date Dec. 3, 1998 Sec. 102(e) Date Dec. 3, 1998 PCT Filed Jun. 5, 1997 PCT Pub. No. WO97/46448 PCT Pub. Date Dec. 11, 1997A covering band (12) is pre-heated and then definitively heated in two subsequent areas (P,Z), and is subjected to primary pulling, in an area (T), where the covering band is pulled and applied to a blister band (1), and to secondary pulling in an area (R) which coincides with the pre-heating area (P). The speed of the covering band (12) is lower in the secondary pulling area (R), so as to determine a lengthening which corresponds at least to its maximum lengthening resulting from pre-heating. Cyclical detecting of reference marks (20) printed on the covering band determines temporary reducing of the covering band (12) speed in the secondary pulling point (R), so as to provoke an additional lengthening. The device includes pulling means (5,11) of the blister band (1) and covering band (12), pre-heating means (11) and heating means (13) for the covering band (12), detecting means (16), and driving means (30) acting with different speeds, controlled by the detecting means (16).