We study the phenomenology of a new minimally extended supersymmetric stand
ard model (nMSSM) where a gauge singlet superfield is added to the MSSR I s
pectrum. The superpotential of this model contains no dimensionful paramete
rs, thus solving the mu. problem of the MSSM. A global discrete R symmetry,
forbidding the cubic singlet self-interaction, imposed on the complete the
ory, guarantees its stability with respect to generated higher-order tadpol
es of the singlet and solves both the domain wall and Peccei-Quinn axion pr
oblems. We give the free parameters of the model and display some general c
onstraints on them. Particular attention is devoted to the neutralino secto
r when a (quasipure) singlino appears to be always the LSP of the model, le
ading to additional cascades, involving the NLSP --> LSP transition, compar
ed with the MSSM. We then present the upper bounds on the masses of the lig
htest and next-to-lightest-when the lightest is an invisible singlet-CP-eve
n Higgs bosons, including the full one-loop and dominant two-loop correctio
ns. These bounds are found to be much higher than the equivalent ones in th
e MSSM. Finally, we discuss some phenomenological implications for the Higg
s sector of the nMSSM in Higgs boson production at future hadron colliders.