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We use the nonlinear dynamics approach for studying delayed feedback optoelectronic oscillators (OEOs) formed by hybrid integration of resonant tunneling diode (RTD) photo-detectors with laser diodes, in both single and dual optical fiber feedback routes. In the single loop topology, the performance of the RTD-OEO free-running self-sustained oscillator is improved in terms of phase noise, with a compromise between the delay line and the strength of the optical re-injection. In the dual-loop configuration, superior performance is achieved due to the suppression of the side modes associated with the optical cavity length, resulting in a side mode suppression ratio of up to -60 dBc of the carrier frequency. We compare experimental results with numerical simulations based on a system of delay differential equations comprising a Liénard oscillator model driven by white Gaussian noise and coupled with laser rate equations. The delayed feedback Liénard oscillator model gives considerable insight into the RTD-OEO dynamical regimes predicting its main features in both single- and dual-loop configurations.