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Microwave properties of high temperature superconductors (HTS) can be strongly affected by RF power levels. Effects of nonlinear phenomena causing this dependence can be modelled using lumped element circuits. We investigated several RLC circuits to model the surface impedance of HTS films, derived equations expressing the transmitted power and assessed models' suitability. Linear, quadratic and exponential dependences of surface resistance RS and inductance LS on the RF magnetic field for the most suitable model have been used in simulations of electromagnetic responses of superconducting films in the Hakki-Coleman dielectric resonator.