  The measurements of the fluxes of atmospheric neutrinos give evidence for the
disappearance of muon neutrinos. The determination of the dependence of the
disappearance probability on the neutrino energy and trajectory allows in
principle to establish unambiguosly the existence of neutrino oscillations.
Alternative mechanisms for the disappearance of the neutrinos have been
proposed, but do not provide a viable description of the data, if one includes
both events where the neutrinos interact in the detector and $\nu$-induced
upward going muons. The proposed mechanisms differ in the energy dependence of
the disappearance probability and the upward going muon data that are produced
by high energy neutrinos give a crucial constraint.
