  We investigate the emergence of oscillations in the decay law of unstable
systems. We discuss in particular the case of the so-called GSI anomaly seen in
the electron capture decays of H-like ions and prove that such oscillations
cannot be explained by neutrino oscillations. We then discuss how such
anomalies could be intimately related to the decay law of unstable systems in
the case in which their spectral function deviates from a Breit-Wigner shape.
