We consider a solution of the atmospheric neutrino problem based on
oscillations of muon neutrinos to sterile neutrinos: νμ↔νs. The zenith angle (Θ) 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 cosΘ=−0.6÷−0.2 and cosΘ=−1.0÷−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.Comment: 14 pages + 9 eps figures in 6 pages, Latex fil