We analyze the MSSM parameter space and discuss the narrow band in the so-called co-annihilation region where sleptons may be long-lived particles. This region is consistent with the WMAP restrictions on the Dark matter and depends on the value of tan β. In this region staus are long-lived and may go through the detector. Due to a relatively small mass (150-850 GeV) their production cross-section at LHC may reach a, few % pb. © World Scientific Publishing Company.