In this research, the Cage-Rotor-Induction-Machine (CRIM) model considering its saturation effect, is investigated. The nonlinear Magnetic-Equivalent-Circuit (MEC) is proposed for machine modeling and nonlinear B-H curve is considered for its saturation effect. However, some current and torque harmonics will be produced due to time and space harmonics combination, which cannot be studied when saturation effect is neglected. For this aim, nonlinear magnetic equations are solved by Newton-Raphson technique. A method is proposed for computing the produced harmonic components and the machine performance is analyzed considering saturation effect. In order to obtain the integrated method, two sample machines (two and also four-pole machines) are modeled and finally the accuracy of the proposed method is verified through the Finite-Element-Method (FEM) via Maxwell software.