  The extrema of the probabilities of the transitions $\nu_{\mu} (\nu_e) \to
\nu_e (\nu_{\mu;\tau})$, $\nu_{2} \to \nu_e$, etc. of neutrinos passing through
a medium consisting of i) two layers of different constant densities or ii)
three layers of constant density, of which the first and the third are
identical but differ in density from the second (e.g., mantle-core-mantle in
the Earth), are analyzed. We show that in addition to the MSW and neutrino
oscillation length resonance (NOLR) local maxima previously discussed, there
exist new resonance-like absolute maxima of interference nature. The latter
correspond to a new effect of total neutrino conversion. The conditions for
existence of the new maxima are fulfilled, in particular, for the
Earth-core-crossing solar and atmospheric neutrinos. We prove that the NOLR and
the new resonance-like enhancement are caused by a maximal constructive
interference between the amplitudes of the neutrino transitions in the
different density layers. The strong resonance-like enhancement of the
transitions in the Earth of the Earth-core-crossing solar and atmospheric
neutrinos is due to the new effect of total neutrino conversion.
