Abstract: Successive stacks of paper sheets are turned during travel along two parallel paths one of which is defined by a first conveyor and the other of which is defined by a set of two or more consecutive conveyors. The speed of the conveyor or conveyors defining one of the paths is greater than the speed of the conveyor or conveyors defining the other path so that the orientation of stacks changes during travel along the two paths. The orientation of successive stacks in at least one intermediate portion of each path is monitored by a battery of photoelectronic detectors whose signals are processed to ascertain whether or not the monitored orientation matches a desired intermediate orientation. The processed signals are used to change the speed of the conveyor or conveyors which define at least one of the paths so as to ensure that each stack assumes a predetermined orientation at the latest on reaching the ends of the two paths.