In this paper,we study a family of non-weight modules over Lie superalgebras S(q)of Block type.We construct and classify the free U(η)-modules of rank 1 over Ramond-Block algebras and free U(4)-modules of rank 2 over Neveu-Schwarz-Block algebras.Moreover,we present the necessary and sufficient conditions for such modules to be simple,and determine their isomorphism classes.The results cover some existing results.
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