This paper presents a new detector for identifying nonlinear mixtures in hyperspectral images. The proposed detector relies on a nonlinear mixing model that approximates the pixel reflectance as a nonlinear combination of pure spectral components contaminated by an additive white Gaussian noise. The parameters involved in the resulting model are estimated using subgradient-based least squares method. A generalized likelihood ratio test is then proposed to decide whether a given pixel results from the commonly used linear mixing model or from a more general nonlinear mixture. The performance of the detection strategy is evaluated thanks to simulations conducted on synthetic data.