Last-generation GAN models allow to generate synthetic images which are visually indistinguishable from natural ones, raising the need to develop tools to distinguish fake and natural images thus contributing to preserve the trustworthiness of digital images. While modern GAN models can generate very high-quality images with no visible spatial artifacts, reconstruction of consistent relationships among colour channels is expectedly more difficult. In this paper, we propose a method for distinguishing GAN-generated from natural images by exploiting inconsistencies among spectral bands, with specific focus on the generation of synthetic face images. Specifically, we use cross-band co-occurrence matrices, in addition to spatial co-occurrence matrices, as input to a CNN model, which is trained to distinguish between real and synthetic faces. The results of our experiments confirm the goodness of our approach which outperforms a similar detection technique based on intra-band spatial co-occurrences only. The performance gain is particularly significant with regard to robustness against post-processing, like geometric transformations, filtering and contrast manipulations.