Most of the methods that have been proposed for speed estimation of induction machines require the rotor and the Stator resistance to change in the normal operating range. On the other hand, estimation of the rotor resistance requires rotor speed. In this paper, after studying conditions for simultaneous estimation of rotor speed and rotor resistance, a method for simultaneous estimation of rotor speed, rotor resistance and stator resistance is proposed. In this method, an additional frequency component is injected to the reference flux and Fast Fourier Transform is used to estimate rotor speed and rotor resistance. Stator resistance is estimated from estimated stator flux using a fuzzy estimator. Finally, effectiveness of the sensorless speed controlled induction machine drive with simultaneous rotor and stator resistance estimation has been verified with simulation results under various operating conditions, especially at low speed and generating conditions.