  We have reconsidered the atmospheric neutrino anomaly in light of the laetst
data from Super-Kamiokande contained events and from Super-Kamiokande and MACRO
up-going muons. We have reanalysed the proposed solution to the atmospheric
neutrino anomaly in terms of non-standard neutrino-matter interactions (NSI) as
well as the standard nu_mu -> nu_tau oscillations (OSC). Our statistical
analysis shows that a pure NSI mechanism is now ruled out at 99%, while the
standard nu_mu -> nu_tau OSC mechanism provides a quite remarkably good
description of the anomaly. We therefore study an extended mechanism of
neutrino propagation which combines both oscillation and non-standard
neutrino-matter interactions, in order to derive limits on flavour-changing
(FC) and non-universal (NU) neutrino interactions. We obtain that the
off-diagonal flavour-changing neutrino parameter epsilon and the diagonal
non-universality neutrino parameter epsilon' are confined to -0.03 < epsilon <
0.02 and |epsilon'| < 0.05 at 99.73% CL. These limits are model independent and
they are obtained from pure neutrino-physics processes. The stability of the
neutrino oscillation solution to the atmospheric neutrino anomaly against the
presence of non-standard neutrino interactions establishes the robustness of
the near-maximal atmospheric mixing and massive-neutrino hypothesis. The best
agreement with the data is obtained for Delta_m^2 = 2.3*10^{-3} eV^2,
sin^2(2*theta) = 1, epsilon = 6.7*10^{-3} and epsilon' = 1.1*10^{-3}, although
the chi^2 function is quite flat in the epsilon and epsilon' directions for
epsilon, epsilon' -> 0.
