  The considerable part of the parameter space in the MSSM corresponding to the
infrared quasi fixed point scenario is almost excluded by LEP II bounds on the
lightest Higgs boson mass. In the NMSSM the mass of the lightest Higgs boson
reaches its maximum value in the strong Yukawa coupling limit when Yukawa
couplings are essentially larger than gauge ones at the Grand Unification
scale. In this limit the solutions of the renormalisation group equations are
attracted to the infrared and Hill type effective fixed lines or surfaces in
the Yukawa coupling parameter space. They are concentrated in the vicinity of
quasi fixed points for $Y_i(0)\to\infty$. However the solutions are attracted
to such points rather weakly. For this reason when all $Y_i(0)\sim 1$ the
solutions of the renormalisation group equations are gathered near a line in
the Hill type effective surface. In the paper the approximate solutions for the
NMSSM Yukawa couplings are given. The possibility of $b$--quark and
$\tau$--lepton Yukawa coupling unification at the scale $M_{X}$ is also
discussed.
