Control device, employing a follower member and a camtrack, for an element of a container processing machine, comprising two camtracks defined by a single rigid assembly, and means for producing relative movement between the follower member and the rigid assembly, between at least two positions, the follower member engaging with a first camtrack in a first position, and with a second camtrack in a second position. Blow moulding or stretch blow moulding comprising at least one such device, notably for controlling the movement of the elongation rod, or for locking/unlocking moulds, or for opening/closing moulds.