In the case of a spinning machine with spinning stations preferably arranged on both sides of the machine, depositing sites for several rows of cans containing the sliver to be spun are assigned to each side of the machine while leaving an aisle. In a roof-type manner, transport devices extend over the operating aisle by means of which the slivers are taken out of the cans and are fed to the spinning stations. The transport devices have two transport sections respectively which are connected with one another by way of a deflecting guide.