Two on-line identifiers of the rotor parameters of the field-oriented (FO) induction motor drive are presented in this paper. The synthesis procedure of the identifiers is based on the model reference adaptive control (MRAC) system theory. An appropriate choice of the reference model allows building a Lyapunov function by means of which the updating law of the rotor time constant can be found. A higher order identifier is also synthesized using hyperstability approach. It allows the simultaneous identification of two rotor parameters. The parameters’ convergence is assured thanks to the persistent exciting propriety of the input vector of the identifier, represented by the stator current. Experimental results conducted on an FO-controlled drive, using a digital signal processor (DSP)-based system (TMS320C31), having 40-MHz clock frequency, show the convergent trajectories of the parameters and of the state errors under various significant steady state and transient operating conditions and for different values of the adaption gains. The results show the satisfactory behavior of the proposed identification algorithms.