Active magnetic bearing (AMB) becomes widely used in various kinds of rotating machinery. However, as the magnetic force is nonlinear, nonlinear phenomena may occur when the rotating speed becomes high and delays of electric current or magnetic flux in the AMB relatively increase. In this paper, the magnetic force in the AMB is modeled by considering both the second-order delay of the electric current and the first-order delay of the magnetic flux. The magnetic flux in the AMB is represented by a power series function of the electric current and shaft displacement, and its appropriate representation for AMB is discussed. Furthermore, by using them, the nonlinear theoretical analysis of the rigid rotor system supported by the AMB is demonstrated. The effects of the delays and other AMB parameters on the nonlinear phenomena are clarified theoretically, and they are confirmed experimentally.