In this short paper we propose a procedure to adjust on-line the rotor time constant estimate of an indirect field-oriented control law for current-fed induction machines. The resulting scheme is shown to be semiglobally exponentially stable provided the load torque on the motor is zero and the a priori uncertainty on the range of variation of the rotor time constant is smaller than 100%. The latter is a reasonable assumption in many practical cases. We also show that, when the load torque is different from zero, the speed error enters in finite time a residual set whose size is proportional to the load torque.