  Non-standard neutrino-nucleon interaction is formulated and explored within
the energy range of quasi-elastic scattering. In particular, the study focuses
on the neutral-current elastic (anti)neutrino scattering off nucleons described
by the exotic reactions $\nu_\alpha ({\bar \nu}_\alpha) + n \rightarrow
\nu_\beta ({\bar \nu}_\beta) + n $ and $ \nu_\alpha ({\bar \nu}_\alpha) + p
\rightarrow \nu_\beta ({\bar \nu}_\beta) + p$, which provide corrections to the
dominant Standard Model processes. In this context, it is shown that the
required exotic nucleon form factors may have a significant impact on the
relevant cross sections. Besides cross sections, the event rate is expected to
be rather sensitive to the magnitude of the lepton-flavour violating parameters
resulting in an excess of events. The overlap of non-standard interactions and
strange quark contributions, in the region of few GeV neutrino energies, is
also examined. The formalism is applied for the case of the relevant
neutrino-nucleon scattering experiments (LSND, MiniBooNE, etc.) and motivates
the notion that such facilities have high potential to probe NSI.
