Atsushi IKEDA Title: On the Hodge structures of double coverings of Kummer surfaces Abstract: We start from an irreducible curve of self-intersection number 4 on an abelian surface. It gives an elliptic pencil on the Kummer surface of the dual abelian surface. We consider a double covering of the Kummer surface branched along a member of the elliptic pencil. Then the elliptic pencil provides a family of the double coverings. We show that the Hodge structures on the second cohomology groups are constant in this family, and we have a failure of the Torelli theorem for the surfaces.