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Resonant and repetitive controllers are well suited for single-phase grid-connected inverters due to their optimum tracking and harmonic rejection capability. In particular, in this paper, their application for single-phase photovoltaic systems is considered. The effects of nonlinear inductance on the performance of current controllers designed to track periodic signals and/or to compensate periodic disturbances are investigated. When the inductance has a nonlinear behavior, a distorted current waveform is produced. Two different nonlinearities have been considered: saturation for high currents and a light nonlinearity, which occurs in the first portion of the magnetization curve, for low currents. A current-dependent model of the nonlinear inductance has been developed. It is mathematically based on the Volterra-series expansion, and it allows us to prove how the harmonic compensation provided by resonant and repetitive controllers can also mitigate the effects of the inductance saturation. This result is the main contribution of this paper, and it is also substantiated with experimental evidence. Moreover, the repetitive controller is able to comply with the harmonic limits reported in IEEE 1547 and IEC 61727, even in very hard saturation conditions.