Abstract: A variable speed driving apparatus drives a plurality of induction machines that facilitates reducing the deviations of the primary magnetic fluxes of the induction machines from the reference and preventing the torque and rotating speed of each induction machine from lowering in the low speed range or when the loads on the respective induction machines are unbalanced. The variable speed driving apparatus includes an inverter 1, induction machines 2, current detectors 3, speed detectors 4, a reference angular frequency operating device 6 for operating the rotating angular frequency of the induction machine bearing the heaviest load based on the output signals of the speed detectors 4, a first phase difference operating device 7.sub.1, for operating the first phase difference between the secondary side component of a reference current and a primary reference magnetic flux, a first reference slip angular frequency operating device 8.sub.1 , to which the first phase difference is inputted, an adder 12.sub.