Anomalous change detection is an important problem in remote sensing image processing. Detecting not only pervasive but anomalous or extreme changes has many applications for which methodologies are available. This paper introduces a nonlinear extension of a full family of anomalous change detectors based on covariance operators. In particular, this paper focuses on algorithms that utilize Gaussian and elliptically contoured distributions, and extend them to their nonlinear counterparts based on the theory of reproducing kernels in Hilbert spaces. The presented methods generalize their linear counterparts, based on the assumption of either Gaussian or elliptically-contoured distribution. We illustrate the performance of the introduced kernel methods in both pervasive and anomalous change detection problems involving both real and simulated changes in multi and hyperspectral imagery with different resolutions (AVIRIS, Sentinel-2, WorldView-2, Quickbird). A wide range of situations are studied, involving droughts, wildfires, and urbanization in real examples. Excellent performance in terms of detection accuracy compared to linear formulations is achieved, resulting in improved detection accuracy and reduced false alarm rates. Results also reveal that the ellipticallycontoured assumption may be still valid in Hilbert spaces. We provide an implementation of the algorithms as well as a database of natural anomalous changes in real scenarios.