This paper presents an adaptive state observer for a nonlinear induction motor model that accounts for viscous friction. The problem is solved using a modified version of the Dynamic Regressor Extension and Mixing (DREMBAO) method. The main idea is to reduce the original model to a regression-like model, where the vector of unknowns contains unknown parameters and state variables. After this step, it becomes possible to obtain a set of scalar linear equations with respect to the unknown state variables and parameters. Using these equations, parameters are estimated with gradient descent estimator, and state estimation is obtained using the gradient observer. Simulation results of an adaptive observer are presented, which demonstrate the effectiveness of the proposed approach. © 2024 IEEE.