This paper presents an unsupervised algorithm for nonlinear unmixing of hyperspectral images. The proposed model assumes that the pixel reflectances result from a nonlinear function of the abundancevectors associated with the pure spectral components. We assume that the spectral signatures of the pure components and the nonlinear function are unknown. The first step of the proposed method estimates the abundance vectors for all the image pixels using a Gaussian process latent variable model. The endmembers are subsequently estimated using Gaussian process regression. The performance of the unmixing strategy is compared with state-of-the-art unmixing strategies on synthetic data. One of the interesting propertiesof the proposed strategy is its robustness to the absence of pure pixels in the image.