An apparatus for the assembly of grommets on electrical cables for use in an automatic cable-processing machine, which is simple and cost effectively constructed so as to achieve a shorter assembly time, per grommet, and utilizes a step-wise rotatable turning device which includes several mandrels whereby, in a first setting (I), always one grommet is pushed onto a mandrel while in a second setting (II) of the turning device, the grommet is pushed, via a slip-on unit, onto a thicker portion of the mandrel for the purpose of expansion, with an assembly head including a grommet-receiving portion and an expanding portion by means of which, in a further setting (IV) of the turning device, the grommet is pulled from the mandrel, whereby the grommet is held in an expanded state, using the expanding portion and pushed onto the cable.