  In the minimal standard model it is possible to gauge any one of the
following global symmetries in an anomaly free way: (i)$L_{e}-L_{\mu}$, (ii)
$L_{e}-L_{\tau}$ or (iii) $L_{\mu}-L_{\tau}$. If the gauge boson corresponding
to (i) or (ii) is (nearly) massless then it will show up as a long range
composition dependent fifth force between macroscopic objects. Such a force
will also influence neutrino oscillations due to its flavour-dependence. We
show that the latter effect is quite significant in spite of very strong
constraints on the relevant gauge couplings from the fifth force experiments.
In particular, the $L_{e}- L_{\mu,\tau}$ potential of the electrons in the Sun
and the earth is shown to suppress the atmospheric neutrino $\nu_\mu \to
\nu_\tau$ oscillations which have been observed at Super-Kamiokande. The
Super-K data of oscillation of multi-GeV atmospheric neutrinos can be used to
put an upper bound on coupling $\alpha_{e\tau}< 6.4 \times 10^{-52}$ and
$\alpha_{e\mu}< 5.5 \times 10^{-52}$at 90% CL when the range of the force is
the earth-sun distance. This is an improvement by two orders on the earlier
fifth force bounds in this range.
