  We discuss the upper bound on the lightest CP-even Higgs boson mass in the
next-to-minimal supersymmetric standard model within the framework of a low
energy renormalisation group analysis. We find $m_h$ < 146 GeV for $m_t$ = 90
GeV, decreasing to $m_h$ < 123 GeV for $m_t$ = 180 GeV.
