A device for driving the rotor of an auxiliary is mounted on a turbine engine auxiliaries support which includes a pinion for driving the rotor shaft. The device includes a tubular shaft driven by the pinion and supported by a first bearing (18) and a second bearing (19) which are secured to the auxiliaries support (10). The rotor shaft is coaxial with the tubular shaft and a splined coupling portion formed between the rotor shaft and the tubular shaft. By virtue of the invention, mechanical loads of the auxiliary are transmitted to a lesser extent to the rotor shaft support bearings and to the auxiliaries support gear train.