This paper proposes an auto-adaptive current control that makes possible to reduce torque ripples of multi-phase machines in open-circuited phase conditions. Contrary to existing methods, current references are not recomputed and the control scheme used in normal mode is auto-adapted in order to run the machine with open-circuited phases. The number of degrees of freedom of the control scheme is adapted to the number of degrees of freedom of the drive and current controllers are auto-adaptive in order to reject the induced speed-dependent harmonic voltage disturbances that appear in fault-mode. Experimental results are presented to show the effectiveness of the proposed method.