  By explicit solution of the one-loop finiteness conditions for all
dimensionless coupling constants (i.~e., gauge coupling constant as well as
Yukawa and quartic scalar-boson self-interaction coupling constants), two
classes of grand unified theories characterized by renormalization-group beta
functions which all vanish at least at the one-loop level are constructed and
analyzed with respect to the (suspected) appearance of quadratic divergences,
with the result that without exception in all of these models the masses of
both vector and scalar bosons receive quadratically divergent one-loop
contributions.
