In this talk we will study the asymptotic spectral density of a nonlinear random matrix model M=YY* with Y=f(WX), where W and X are random rectangular matrices with iid entries and f is a non-linear smooth function. We will derive a self-consistent equation for the Stieltjes transform of the limiting eigenvalue distribution using the resolvent approach via the cumulant expansion. This is based on a joint work with Dominik Schröder.