  Assuming two-neutrino mixing takes place in vacuum, we study in detail the
conditions under which the $\nu_2 \to \nu_{e}$ and $\nu_{\mu} \to \nu_{e}$
($\nu_e \to \nu_{\mu(\tau)}$) transitions in the Earth are strongly enhanced by
the neutrino oscillation length resonance when the neutrinos cross the Earth
core. We show, in particular, that the neutrino oscillation length resonance is
operative also in the $\bar{\nu}_{\mu} \to \bar{\nu}_{s}$ transitions at small
mixing angles. The properties of the $\nu_2 \to \nu_{e}$ and $\nu_{\mu} \to
\nu_{e}$ ($\nu_e \to \nu_{\mu(\tau)}$) transition probabilities in the
corresponding resonance regions are examined. Some implications of our results
for the transitions of solar and atmospheric neutrinos traversing the Earth
core, relevant for the interpretation of the results of the solar and
atmospheric neutrino experiments, are also discussed.
