An advancing unit for a cleaning spiral, which can be rotated by a motor about its longitudinal axis, of a pipe cleaning machine, such as, for example, a pipe cleaning machine having a drum. The advancing unit includes a drive device, which produces the advancement of the cleaning spiral, with at least two clamping parts, wherein at least one clamping part thereof can be brought into a clamping position against the cleaning spiral in such a manner that the clamping parts press against the cleaning spiral, so that an advancement of the cleaning spiral is generated in the case of a rotating cleaning spiral. The advancing unit further comprises a control device for controlling the advancement of the cleaning spiral by means of at least one of the clamping parts as well as a safety device, by which at least one of the clamping parts can be brought out of its clamping position against the cleaning spiral. It is provided that the control device and the drive device and/or the safety device can be actuated by means of a common handle part. The invention further relates to a pipe cleaning machine, in particular a pipe cleaning machine having a drum, and to a method for operating a pipe cleaning machine.