  The $\mu\nu$SSM is a supersymmetric standard model that accounts for light
neutrino masses and solves the $\mu$ 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 $\mu\nu$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 $\mu\nu$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.
