A nonlinear adaptive speed observer is designed for the sensorless control of induction motors. In order to design the speed observer, the measurements of the stator currents and the estimates of the rotor fluxes are used. The sliding mode cascade observer is designed to estimate the time derivatives of the stator currents. The open-loop observer is designed to estimate the rotor fluxes and its time derivatives using the stator current derivatives. The adaptive observer is also designed to estimate the rotor resistance. Sequentially, the rotor speed is calculated using these estimated values. It is shown that the estimation errors of the corresponding states and the parameters converge to the specified residual set. It is also shown that the speed controller using these estimates is performed well. The simulation examples are represented to investigate the validity of the proposed observers for the sensorless control of induction motors.