A control device, with a follower member and a cam path, to control an element of a container processing machine, comprising two cam paths defined by a single rigid assembly, means enabling a relative movement between the follower member and the rigid assembly, between at least two positions, the follower member engaging a first cam path in a first position, the follower member engaging a second cam path in a second position, wherein the follower member comprises two rollers carried by a common support shaft, the first and second rollers engaging respectively with first and second cam paths in a first position of the common support shaft relative to the rigid assembly, the first and second rollers engaging respectively with third and fourth cam paths in a second position of the shaft relative to the rigid assembly.