  We consider a solution of the atmospheric neutrino problem based on
oscillations of muon neutrinos to sterile neutrinos: $\nu_{\mu}$
$\leftrightarrow$ $\nu_s$. The zenith angle ($\Theta$) dependences of the
neutrino and upward-going muon fluxes in presence of these oscillations are
studied. The dependences have characteristic form with two dips: at $\cos
\Theta = -0.6 \div -0.2$ and $\cos \Theta = -1.0 \div -0.8$. The latter dip is
due to parametric resonance in oscillations of neutrinos which cross the core
of the earth. A comparison of predictions with data from the MACRO, Baksan and
Super-Kamiokande experiments is given.
