  The standard model is extended with three right-handed, singlet neutrinos
with general couplings permitted by the $SU(2)_{L}\times U(1)$ symmetry. The
traditional oscillations are accounted for, as usually, by three left-handed
neutrinos. The article investigates new structures that develop when the masses
of the right-handed states are in the eV range. The new states interfere and
oscillate with the standard light neutrinos. New structures appear when the
detectors average over short wavelengths. I use these results to present and
classify properties of the observed anomalies in the MiniBooNe, reactor and
Gallium-detector experiments.
