  The simplest extension of the MSSM that does not contradict LEP II
experimental bound on the lightest Higgs boson mass at $\tan\beta\sim 1$ is the
modified Next-to-Minimal Supersymmetric Standard Model (MNSSM). We investigate
the renormalization of Yukawa couplings and soft SUSY breaking terms in this
model. The possibility of $b$-quark and $\tau$-lepton Yukawa coupling
unification at the Grand Unification scale $M_X$ is studied. The particle
spectrum is analysed in the vicinity of the quasi-fixed point where the
solutions of renormalization group equations are concentrated at the
electroweak scale.
