In the case of a caterpillar track drawing machine having a drawing die and a caterpillar track disposed behind the drawing die, which track comprises two drawing chains having drawing tools disposed on chain links of the drawing chains, it should be possible to align the drawing tools of at least one of the two drawing chains jointly with the respective chain link, perpendicular to the drawing line, so that the caliber range can be changed, in simple and operationally reliable manner, between two drawing recesses having different caliber ranges. The latter is also possible if two different drawing recesses of the second one of the two drawing chains are intended for a first caliber range for which the first drawing recesses for at least one of the two drawing chains are intended, or if the drawing recesses of a first one of the two drawing chains deviate from the drawing recesses of a second one of the two drawing chains.