This paper investigates the use of Gaussian processes to detect non-linearly mixed pixels in hyperspectral images. The proposed technique is independent of nonlinear mixing mechanism, and therefore is not restricted to any prescribed nonlinear mixing model. The observed reflectances are estimated using both the least squares method and a Gaussian process. The fitting errors of the two approaches are combined in a test statistics for which it is possible to estimate a detection threshold given a required probability of false alarm. The proposed detector is compared to a robust nonlinearity detector recently proposed using synthetic data and is shown to provide a better detection performance. The new detector is also tested on a real hyperspectral image.