A multi-step transmission having a housing which accommodates eight shafts and four planetary gear sets, and at least six shift elements including brakes and clutches which are engaged to implement different ratios between a drive shaft and output shaft. The carrier of gearset (4) is connected to shaft (14) which is connectable, via brake (8), to the housing and, via clutch (11), to shaft (15) which is coupled to the ring gear of gearset (6). The shaft (16) connects the ring gear of gearset (5) to the sun gear of gearset (6) and is couplable, via a clutch (12), to the output shaft. The shaft (17) is connected to the ring gear of gearset (4) and the drive shaft is connectable, via clutch (13), to shaft (14) and is coupled to the carrier of gearset (5).