Autonomous oscillators, such as clocks and lasers, produce periodic signals without any external frequency reference. In order to sustain stable periodic motion, there needs to be an external energy supply as well as nonlinearity built into the oscillator to regulate the amplitude. Usually, nonlinearity is provided by the sustaining feedback mechanism, which also supplies energy, whereas the constituent resonator that determines the output frequency stays linear. Here, we propose a new self-sustaining scheme that relies on the nonlinearity originating from the resonator itself to limit the oscillation amplitude, while the feedback remains linear. We introduce a model for describing the working principle of the self-sustained oscillations and validate it with experiments performed on a nonlinear microelectromechanical oscillator.