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The methodology for the nonlinear modelling and analysis of active magnetic bearing (AMB) systems in the harmonic domain (HD) is presented. This approach is based on the HD linearisation of the AMB system around nonlinear stationary solutions at different rotating speeds. The main advantage obtained is the representation of the periodic LTV models that describe the steady-state dynamics for each speed, by means of LTI models in the HD. In order to show its possibilities, the proposed approach is applied to an AMB laboratory testbed based on the MBC500 Rotor Dynamics from Launchpoint Technologies. This analysis explains the nonlinear nature of the response that appears at high speeds, due to the large oscillations introduced by the shaft unbalance, and detects a low-frequency gain loss when increasing the rotating speed. This phenomenon causes the instability of the system, leading to destructive crashes. In addition, the analysis allows to take into account the effect of the delay introduced by the calculation time in the system behaviour when the controller is implemented by using digital devices.