A thread stitching machine to process signatures into book blocks includes a transport system for the signatures including a transport section on which the signatures are straddling for supply to a stitching station. The transport section includes an auxiliary saddle and a driven, continuously moving conveying chain to drive the auxiliary saddle. The conveying chain has spaced-apart, integrated pusher elements. A downstream installed stitching station includes a freely moving stitching saddle immediately following the auxiliary saddle. The stitching saddle includes a separate conveying device for the signatures, operated by a drive. A detection device is arranged at a transition between the auxiliary saddle and the stitching saddle to detect a position of the signature and a time which the signature passes by. The conveying chain is operated with a change in speed that depends on different sheet lengths following each other directly in a sequence of signatures.