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We show that the Li problems can be solved in the next-to-minimalsupersymmetric standard model where the slepton as the next-to-lightest SUSYparticle is very long-lived. Such a long-lived slepton induces exotic nuclearreactions in big-bang nucleosynthesis, and destroys and produces the $^7$Li and$^6$Li nuclei via bound state formation. We study cases where the lightest SUSYparticle is singlino-like neutralino and bino-like neutralino to presentallowed regions in the parameter space which is consistent with theobservations on the dark matter and the Higgs mass.

Big-bang nucleosynthesis through bound-state effects with a long-lived slepton in the NMSSM