to the MSSM (minimal supersymmetric extension of the Standard Model) has been motivated by several issues: (i) the solution of the so-called $\mu $-problem; (ii) the possibility of spontaneous breaking of the CP symmetry; (iii) the upper limits on the Higgs mass that are relatively low in the MSSM could be relaxed; (iv) the neutral particle spectrum is enriched by two scalars and one fermion, which could mix with other Higgs bosons and neutralinos and modify their physical properties; (v) possible deviations from the MSSM could urge to enlarge the experimental searches, which have been centred upon the MSSM. We refer here to the supersymmetric model with a gauge singlet in its simplest version, as defined below, as the (M+1)SSM.

However, according to our analysis, the strong constraints from LEP experiments, when combined with theoretical and phenomenological requirements, select the (M+1)SSM parameters in such a way that the gauge singlet scalars and fermions are basically decoupled and the rest of the spectrum effectively reproduces a restricted class of the MSSM. Because of this similarity, the motivations (ii)-(v) fade out as these issues are excluded or diminished after such a detailed investigation. Nevertheless, this also means that phenomenological analyses of the 