A multi-step transmission including four gear sets, shafts, and shifting elements. The sun gear of gearset (P4) couples shaft (3) which communicates, via brake (03), with the housing. The carrier of gearset (P4) couples the output shaft, which couples the ring gear of gearset (P2). The ring gear of gearset (P4) couples shaft (7), which couples the carrier of gearset (P2) and, via clutch (17), communicates with the drive shaft, which communicates, via clutch (18), with the ring gear of gearset (P1) coupled to shaft (8), and, via clutch (15), communicates with shaft (5). Shaft (5) couples the sun gear of gearset (P3), and, via brake (05), communicates with the housing. The carrier of gearset (P1) couples the shaft (6), the ring gear of gearset (P3) and the sun gear of gearset (P2). The carrier of gearset (P3) couples the shaft (4), which, via brake (4), communicates with the housing.