  We investigate the collider signatures of neutral and charged Long-Lived
Particles (LLPs), predicted by the Supersymmetric $B-L$ extension of the
Standard Model (BLSSM), at the Large Hadron Collider (LHC). The BLSSM is a
natural extension of the Minimal Supersymmetric Standard Model (MSSM) that can
account for non-vanishing neutrino masses. We show that the lightest
right-handed sneutrino can be the Lightest Supersymmetric Particle (LSP), while
the Next-to-the LSP (NLSP) is either the lightest left-handed sneutrino or the
left-handed stau, which are natural candidates for the LLPs. We analyze the
displaced vertex signature of the neutral LLP (the lightest left-handed
sneutrino), and the charged tracks associated with the charged LLP (the
left-handed stau). We show that the production cross sections of our neutral
and charged LLPs are relatively large, namely of order ${\cal O}(1)~{\rm fb}$.
Thus, probing these particles at the LHC is quite plausible. In addition, we
find that the displaced di-lepton associated with the lightest left-handed
sneutrino has a large impact parameter that discriminates it from other SM
leptons. We also emphasize that the charged track associated with the
left-handed stau has a large momentum with slow moving charged tracks, hence it
is distinguished from the SM background and therefore it can be accessible at
the LHC.
