We consider the possibility of getting relatively light long-lived supersymmetric particles within the framework of the MSSM with gravity mediated SUSY breaking. It is shown that for the particular choice of parameters this possibility can be realized in the co-annihilation region with light staus, in the region with large negative trilinear scalar coupling A distinguished by light stops, and in the focus-point region where light charginos may be long-lived. It requires the fine-tuning of parameters, however the sit- uation can take place in the constrained MSSM along the border LSP-NLSP lines. The phenomenology of the long-lived superparticles at the LHC is discussed.