Supersymmetric Higgs Bosons at the Limit

Using a combination of renormalisation group and effective potential methods, we discuss the bound on the lightest CP-even Higgs boson mass $m_h$ in the next-to-minimal supersymmetric standard model. We find $m_h\leq 146,139,149 \ GeV$ for $m_t=90,140,190 \ GeV$.