The $����$SSM is a supersymmetric standard model that accounts for light neutrino masses and solves the $��$ problem of the MSSM by simply using right-handed neutrino superfields. Since this mechanism breaks R-parity, a peculiar structure for the mass matrices is generated. The neutral Higgses are mixed with the right- and left-handed sneutrinos producing 8$\times$8 neutral scalar mass matrices. We analyse the Higgs sector of the $����$SSM in detail, with special emphasis in possible signals at colliders. After studying in general the decays of the Higges, we focus on those processes that are genuine of the $����$SSM, and could serve to distinguish it from other supersymmetric models. In particular, we present viable benchmark points for LHC searches. For example, we find decays of a MSSM-like Higgs into two lightest neutralinos, with the latter decaying inside the detector leading to displaced vertices, and producing final states with 4 and 8 $b$-jets plus missing energy. Final states with leptons and missing energy are also found.

Final version to appear in JHEP. The discussion on signals at colliders, expanded. 33 pages, 8 figures and 9 tables