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

Quasi-fixed point scenarios and the Higgs mass in the E6 inspired SUSY models