A calculation of the probability of recoilless emission and detection of neutrinos (Moessbauer effect with neutrinos) which takes into account the boundedness of the parent and daughter nuclei in the neutrino source and detector as well as the leptonic mixing is presented. It is shown that, despite their near monochromaticity, the recoilessly emitted and captured neutrinos should oscillate. Our calculation permits quantitative predictions of the transition rate in future experiments, and shows that the decoherence and delocalization factors, which could in principle suppress neutrino oscillations, are irrelevant under realistic experimental conditions.