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A main aim of this talk is to show that there exits a nontrivial superextention of de Sitter and anti-de Sitter Lie algebras simultaneously. Using the standard contraction procedure for this superextension we obtain an Z_2×Z_2-graded superalgebra which contains simultaneously standard (Z_2-graded) and alternative (Z_2×Z_2-graded) super-Poincar´e algebras with N = 2,4, . . . supercharge multiplets.