  The tree level potential for a scalar multiplet of `Yukawa fields' $Y$ for
one type of quarks admits the promising vacuum configuration $<Y> \propto {\rm
diag}(0,0,1)$ that breaks spontaneously $SU(3)_L\times SU(3)_R$ flavour
symmetry. We investigate whether the vanishing entries could be lifted to
nonvanishing values by slightly perturbing the potential, thus providing a
mechanism to generate the Yukawa hierarchies. For theories where at the lowest
order the only massless states are Nambu-Goldstone bosons we find, as a general
result, that the structure of the tree-level vacuum is perturbatively stable
against corrections from scalar loops or higher dimensional operators. We
discuss the reasons for this stability, and give an explicit illustration in
the case of loop corrections by direct computation of the one-loop effective
potential of Yukawa fields. Nevertheless, a hierarchical configuration
$<Y>\propto {\rm diag}(\epsilon',\epsilon,1)$ (with $\epsilon', \epsilon\ll 1$)
can be generated by enlarging the scalar Yukawa sector. We present a simple
model in which spontaneous breaking of the flavour symmetry can give rise to
the fermion mass hierarchies.
