Device for moulding thermoplastic containers by blow-moulding or stretch blow-moulding hot preforms, said device comprising a mould and blowing means comprising a blowing nozzle of the bell-nozzle type which is axially displaceable and driving means for displacing said blowing nozzle above said mould between a raised position in which the end of the nozzle is raised above the mould and a blowing position in which the end of the nozzle is in sealing abutment against the mould, which driving means comprise mechanical driving means including at least one cam follower roller integral with the nozzle, and at least one respective control cam against which said cam follower roller is maintained in abutment, the cam follower roller and the cam being in relative movement, characterized in that the driving means further comprise pneumatic driving means which include: - a fixed enclosure surrounding substantially coaxially an upper terminal section of the blowing nozzle, - a piston enclosed in said enclosure and integral with the upper end of the blowing nozzle, said piston defining in the enclosure an upper chamber and a lower chamber, the piston having an upper face of which the surface area is greater than the surface area of the bell of the nozzle and a lower face having a surface area which is less than the surface area of its upper face, - an upper orifice provided in the enclosure and in communication with the upper chamber, - a lower orifice provided in the enclosure and in communication with said lower chamber, - said two upper and lower orifices (22, 23) being connected to a source of pressurized control fluid, - a bypass circuit extending between said two upper and lower chambers (19, 20), and - selector means (26, 26') capable of separating said lower orifice from, and connecting said lower orifice to, the atmosphere during the blow-moulding phase, - the surface area of the upper face of the piston being such that the force exerted on the piston by the control fluid is greater than the force in the reverse direction exerted by the blowing fluid on the bell of the nozzle, whereby it is the mechanical driving means with the cam follower roller in abutment against the cam which determine the speed of displacement of the nozzle, whilst the pneumatic driving means ensure the maintenance of the cam follower roller in abutment against the cam during the displacement of the nozzle and the locking of the nozzle in abutment against the mould during the blow-moulding phase, and whereby it also becomes possible that the pressurized fluid controlling the operation of the pneumatic driving means is not systematically discharged into the atmosphere and that the dead volumes may be reduced, making possible substantial savings in pressurized blowing fluid. - a fixed enclosure surrounding substantially coaxially an upper terminal section of the blowing nozzle, - a piston enclosed in said enclosure and integral with the upper end of the blowing nozzle, said piston defining in the enclosure an upper chamber and a lower chamber, the piston having an upper face of which the surface area is greater than the surface area of the bell of the nozzle and a lower face having a surface area which is less than the surface area of its upper face, - an upper orifice provided in the enclosure and in communication with the upper chamber, - a lower orifice provided in the enclosure and in communication with said lower chamber, - said two upper and lower orifices (22, 23) being connected to a source of pressurized control fluid, - a bypass circuit extending between said two upper and lower chambers (19, 20), and - selector means (26, 26') capable of separating said lower orifice from, and connecting said lower orifice to, the atmosphere during the blow-moulding phase, - the surface area of the upper face of the piston being such that the force exerted on the piston by the control fluid is greater than the force in the reverse direction exerted by the blowing fluid on the bell of the nozzle,