In this paper we present two different sequent calculi for modal logic S5, each of which reflects, at the syntactic level, one of the two ways of describing S5 semantically. We will analyze both these sequent calculi in detail and we will briefly sketch the proofs of: (i) adequacy of the calculi, (ii) admissibility of the structural rules, cut-rule included. All results are proved in a purely syntactic way. Contraction-free, Cut-free, Modal logic, Sequent Calculus, Tree-hypersequents
