  A theoretical analysis of solutions of renormalisation group equations in the
MSSM corresponding to the quasi-fixed point conditions shows that the mass of
the lightest Higgs boson in this case does not exceed $94\pm 5\text{GeV}$. It
means that a substantial part of the parameter space of the MSSM is practically
excluded by existing experimental data from LEP II. In the NMSSM the upper
bound on the lightest Higgs boson mass reaches its maximum in the strong Yukawa
coupling regime, when Yukawa constants are considerably larger the gauge ones
on the Grand Unification scale. In this paper a particle spectrum in a simple
modification of NMSSM which leads to a self-consistent solution in the
considered region of the parameter space is studied. This model allows one to
get $m_h\sim 125\text{GeV}$ even for comparatively low values of $\tan\beta\ge
1.9$. For an analysis of the Higgs boson spectrum and neutralino spectrum a
method for diagonalisation of mass matrices proposed formerly is used. The mass
of the lightest Higgs boson in this model does not exceed $130.5\pm
3.5\text{GeV}$.
