The paper discusses two observer designs for estimation of the inverse of the rotor time constant of the induction motor. The paper presents the model and develops a linear and a sliding-mode observer. Estimation is based on the dynamic equation of the flux magnitude in the rotating reference frame. The stationary-frame fluxes are obtained using a voltage model observer -They are used for field orientation and also to compute the flux magnitude. Based on the measured voltages, currents, and with known flux, the paper estimates the rotor time constant inverse using a Pseudo-MRAS sliding mode observer. The paper also presents a linear observer, however, it is shown that this design does not perform. The method proposed is simple and is not highly computational. The sensitivity of the observer to the input quantities and motor parameters is studied. The theory is validated by computer simulations and experimental tests.