  We analyse the two-loop renormalization group (RG) flow of the gauge and
Yukawa couplings within the E6 inspired supersymmetric (SUSY) models with extra
U(1)_{N} gauge symmetry under which right-handed neutrinos have zero charge. In
these models single discrete \tilde{Z}^{H}_2 symmetry forbids the tree-level
flavor-changing transitions and the most dangerous baryon and lepton number
violating operators. We consider two different scenarios A and B that involve
extra matter beyond the MSSM contained in three and four 5+\overline{5}
representations of SU(5) respectively plus three SU(5) singlets which carry
U(1)_{N} charges. In the scenario A the measured values of the SU(2)_W and
U(1)_Y gauge couplings lie near the fixed points of the RG equations. In the
scenario B the contribution of two--loop corrections spoils the unification of
gauge couplings resulting in the appearance of the Landau pole below the Grand
Unification scale M_X. The solutions for the Yukawa couplings also approach the
quasi fixed points with increasing their values at the scale M_X. We calculate
the two--loop upper bounds on the lightest Higgs boson mass in the vicinity of
these quasi fixed points and compare the results of our analysis with the
corresponding ones in the NMSSM. In all these cases the theoretical
restrictions on the SM--like Higgs boson mass are rather close to 125 GeV.
