Abstract Recently, a novel identification method for a nonlinear dynamic model, called nonlinear Linear Fractional Representation (NL-LFR) model, has been developed. The model, composed of a static nonlinearity (SNL) surrounded by linear dynamics, can account for both nonlinear feed-forward and nonlinear feed-back effects. Using two classical frequency response measurements, the SNL is automatically recovered in a user-friendly and efficient (non-iterative) way. In this contribution, the method is illustrated on a glucoregulatory benchmark dataset (insulin–glucose relationship of the human body). The research on insulin–glucose models is essential to develop methodologies to control the blood glucose level in diabetes patients. The obtained results outperform earlier results on the same benchmark data, while providing an excellent accuracy-complexity tradeoff.