  The formalism of non-standard four-fermion interactions provides a
convenient, model-independent way of parameterizing a wide class of ``new
physics'' scenarios. In this article, we study the performance of reactor and
superbeam neutrino experiments in the presence of such non-standard
interactions (NSI). Due to interference between the standard and non-standard
amplitudes, sizeable effects are to be expected if the NSI parameters are close
to their current upper limits. We derive approximate formulas for the relevant
oscillation probabilities including NSI, and show how the leading effects can
be understood intuitively even without any calculations. We will present a
classification of all possible NSI according to their impact on reactor and
superbeam experiments, and it will turn out that these experiments are highly
complementary in terms of their sensitivity to the non-standard parameters. The
second part of the paper is devoted to detailed numerical simulations, which
will demonstrate how a standard oscillation fit of the mixing angle theta-13
may fail if experimental data is affected by NSI. We find that for some
non-standard terms, reactor and superbeam experiments would yield seemingly
conflicting results, while in other cases, they may agree well with each other,
but the resulting value for theta-13 could be far from the true value. This
offset may be so large that the true theta-13 is even ruled out erroneously. In
the last section of the paper, we demonstrate that reactor and superbeam data
can actually establish the presence of non-standard interactions. Throughout
our discussion, we pay special attention to the impact of the complex phases,
and of the near detectors.
