  We analyze the implications of the infrared quasi fixed point solution for
the top quark mass in the Minimal Supersymmetric Standard Model. This solution
could explain in a natural way the relatively large value of the top quark mass
and, if confirmed experimentally, may be suggestive of the onset of
nonperturbative physics at very high energy scales. In the framework of grand
unification, the expected bottom quark - tau lepton Yukawa coupling unification
is very sensitive to the fixed point structure of the top quark mass. For the
presently allowed values of the electroweak parameters and the bottom quark
mass, the Yukawa coupling unification implies that the top quark mass must be
within ten percent of its fixed point values.
