In this study, linear and nonlinear vibration movements of simply supported stepped microbeams placed in a magnetic field have been analyzed using Modified Couple Stress Theory. By taking into account the step radius ratio, step-change position, and material size parameter, the equations of motion of the stepped-microbeam are obtained using the Hamilton principle. The resulting equations of motion are nondimensionalized to eliminate dependence on material type and geometric structure. The approximate solution of the dimensionless equations of motion is calculated using the method of multiple scales, one of the perturbation methods. The solution stages of the study are divided into two separate parts as linear and nonlinear problems. Firstly, the linear issue of the stepped microbeam is addressed. The natural frequencies of the system are derived by solving the linear problem. Linear and nonlinear effects of step radius ratio, step-change position, and microbeam coefficient are investigated and frequency-amplitude graphs are presented. The resonance state where forcing frequency is equal to natural frequency is examined and stability analysis has been made.