<p>Blind system identification is an issue that has been thoroughly examined in numerous works and has attracted a lot of interest from the scientific community. The linear case has been the subject of most of the current research, but nonlinear system identification has also received a lot of attention. In this work, we tackle the topic of employing cumulants obtained from the system output to identify the kernels of nonlinear systems. In particular, we use higher-order cumulants (HOC) to propose a novel extension of the linear-to-nonlinear relationship. To identify the kernels of nonlinear quadratic systems, two novel blind identification approaches are developed. While the second approach only uses fourth-order cumulants that are obtained from the quadratic system’s output, the first approach combines second- and third-order cumulants. It is assumed that the system’s input is a stationary, non-Gaussian, independent and identically distributed (i.i.d.). Numerical simulations on a nonlinear quadratic model were performed in order to verify the proposed approaches. 200 Monte Carlo simulations at different signal-to-noise ratio (SNR) levels are included in the evaluation to show how robust and convergent the developed approaches are in noisy environments. The outcomes demonstrate the efficacy of the proposed blind identification approaches and are in good agreement with the body of existing literature.</p>