There is described a unit (3) for sterilizing a web (2) of packaging material, the unit having a bath (5) containing a sterilizing agent in which the web (2) is advanced continuously and an aseptic environment (27) containing sterile air, connected to an outlet (10) of the bath (5). and housing drying means (15) for removing residual sterilizing agent from the web (2) the aseptic environment (27) is divided into two regions (23. 6) by a narrow-section channel (28), along which the web (2) travels, and which is sized to produce a predetermined difference in pressure between the two regions (23. 6). and so force air into the channel (28) from the higher- pressure region (23) to the lower-pressure region (6) to dry the web (2).