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In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras L and a class of Block type Lie algebras B(q), where q is a nonzero complex number. We determine those modules whose restriction to the Cartan subalgebra (modulo center) are free of rank one.We also provide a sufficient and necessary condition for such modules to be simple, and determine their isomorphism classes. Moreover, we obtain the simplicity of modules over loop-Virasoro algebras by taking tensor products of some irreducible modules mentioned above with irreducible highest weight modules or Whittaker modules. 12 C, ∀ i, j ∈ Z,

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In this paper, we construct a family of non-weight modules over the super-Virasoro algebras. Those modules when regarded as modules of the Ramond algebra and further restricted as modules over the Cartan subalgebra h are free of rank 1, while when regarded as modules of the Neveu-Schwarz algebra and further restricted as modules over the Cartan subalgebra H are free of rank 2. We obtain a sufficient and necessary condition for such modules to be simple. Moreover, we determine the isomorphism classes of these modules. Finally, we show that these modules constitute a complete classification of free U (h)-modules of rank 1 over the super-Virasoro algebra of Ramond type, and also constitute a complete classification of free U (H)-modules of rank 2 over the super-Virasoro algebra of Neveu-Schwarz type.