  In a model where quark and lepton masses and family-mixings are caused not by
a variety of Yukawa couplings $y_{ij}$ ($i,j=1,2,3$: family indices) with one
vacuum expectation value (VEV) $v=\langle\phi_L^0\rangle_0$, but by a variety
of VEV's of a U(3)-family nonet Higgs boson $\phi_L$, $v_{i}^j=\langle\phi_{L
i}^{0j}\rangle_0$, with a single coupling constant, the following problems are
investigated: what constraints on the Higgs potential are imposed in order to
provide realistic quark and lepton mass spectra and mixings and what
constraints on the Higgs boson masses are required in order to suppress
unwelcome flavor-changing neutral current effects. Lower bounds of the physical
Higgs boson masses of $\phi_L$ are deduced from the present experimental data
and new physics from the present scenario is speculated.
