  The SuperKamiokande atmospheric neutrino measurements leave substantial room
for nonstandard interactions (NSI) of neutrinos with matter in the nu_e- nu_tau
sector. Large values of the NSI couplings are accommodated if the vacuum
oscillation parameters are changed from their standard values. Short and medium
baseline neutrino beams can break this degeneracy by measuring the true vacuum
oscillation parameters with the muon neutrino disappearance mode, for which the
matter effects are negligible or subdominant. These experiments can also search
for the nu_e-nu_tau flavor changing effects directly, by looking for
nu_mu->nu_e conversion caused by the intervening matter. We discuss both of
these methods for the case of MINOS. We find that, while the present MINOS data
on nu_mu disappearance induce only minor changes on the constraints on the NSI
parameters, the situation will improve markedly with the planned increase of
the statistics by an order of magnitude. In that case, the precision will be
enough to distinguish certain presently allowed NSI scenarios from the no-NSI
case. NSI per quark of about 10% the size of the standard weak interaction
could give a nu_mu - nu_e conversion probability of the order ~ 10^{-2},
measurable by MINOS in the same high statistics scenario. In this nu_mu - nu_e
channel, the small effects of NSI could be comparable or larger than the vacuum
contribution of the small angle theta_{13}. The expected theta_{13} bound at
MINOS should be more properly interpreted as a bound in the theta_{13}-NSI
parameter space.
