Stability, robustness, and estimation accuracy of the adaptive flux observer (AFO) for sensorless induction motor (IM) drives are the most critical issues at zero and very low frequencies. In this paper, the design of speed, stator resistance, and rotor resistance estimators, to improve the robustness of AFO to parameters variation, is proposed. These estimators are arranged to have a cascade multi-input multi-output structure, and simplified to a single-input single-output structure for stability analysis and gain selections. To design both the observer feedback gains and adaptive proportional-integral gains, the stability conditions of the estimators are derived to guarantee a stable AFO in all the four quadrants of operation. The sensitivity analysis against stator and rotor resistance variations is also provided. The detailed analytical, simulation, and experimental results are presented to validate the proposed AFO of sensorless IM drives in torque- and speed-controlled modes of operation, particularly at zero and very low frequencies.