We give an explicit component Lagrangian construction of massive higher spin on-shellN=1supermultiplets in four-dimensional Anti-de Sitter spaceAdS4. We use a frame-like gauge invariant description of massive higher spin bosonic and fermionic fields. For the two types of the supermultiplets (with integer and half-integer superspins) each one containing two massive bosonic and two massive fermionic fields we derive the supertransformations leaving the sum of four their free Lagrangians invariant such that the algebra of these supertransformations is closed on-shell.
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