We present a novel method for segmenting nonstationary textures. Our approach uses a multidimensional AM-FM representation for the texture, and provides the FM features to an SOFM-LVQ neural network system that performs the segmentation. For the segmentation, we use the eigenvalues of the instantaneous frequency gradient tensor, and show how these eigenvalues capture the non-stationary structure of a texture. For a woodgrain image, the segmentation results are shown to capture the essential non-stationary nature of the grain.