  We consider dilatonic brane-world models with a non-minimal coupling between
a dilaton and usual matter on a brane. We demonstrate that variation of the
fundamental constants on the brane due to such interaction leads to strong
restrictions on parameters of models. In particular, the experimental bounds on
variation of the fine structure constant rule out non-minimal dilatonic models
with a Liouville-type coupling potential f(varphi) = exp (b varphi) where b is
order of 1.
