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,

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type A 1 by taking tensor products of irreducibles defined in [7] with irreducible highest weight modules. The irreducibility and the isomorphism classes of these modules are determined. Moreover, we show that these tensor product modules are different from the known non-weight modules. Finally, we realize some tensor product modules as induced modules from modules over certain subalgebras of the affine-Virasoro algebra of type A 1 , and give sufficient and necessary conditions for these induced modules to be reducible.