In this paper we address the problems of observer design for induction motors (IM). The rotor resistance and load torque are supposed to be unknown. The only measured signals are stator current and control voltage. The approach is based on a new way of applying Dynamic Regressor Extension and Mixing method (DREM) to regression models with non-stationary parameters. Firstly, using partial changes of coordinates and filtering technique, IM model is represented in regression-like form. Applying DREM yields relations, which are used to construct flux observer and rotor resistance estimator. On the next step proposed method is applied again to obtain speed and load torque estimates. The proposed speed observer design can be also applied to the permanent magnet synchronous motors.