  The multiple point criticality principle is applied to the pure Standard
Model (SM), with a desert up to the Planck scale. We are thereby led to impose
the constraint that the effective Higgs potential should have two degenerate
minima, one of which should have a vacuum expectation value of order unity in
Planck units. In this way we predict a top quark mass of $173 \pm 5$ GeV and a
Higgs particle mass of $135 \pm 9$ GeV. The quark and lepton mass matrices are
considered in the anti-grand unified extension of the SM based on the gauge
group $SMG^3 \otimes U(1)_f$; this group contains three copies of the SM gauge
group SMG, one for each generation, and an abelian flavour group $U(1)_f$. The
9 quark and lepton masses and 3 mixing angles are fitted using 3 free
parameters, with the overall mass scale set by the electroweak interaction. It
is pointed out that the same results can be obtained in an anomaly free $SMG
\otimes U(1)^3$ model.
