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It is shown that in transitively self-similar spatially homogeneous tiltedperfect fluid models the symmetry vector is not normal to the surfaces ofspatial homogeneity. A direct consequence of this result is that there are noself-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore themost general Bianchi VIII and IX spacetime which admit a four dimensional groupof homotheties is given.Comment: 5 pages, Latex; One reference and minor clarifications added. To  appear in General Relativity and Gravitatio

Letter: Self-Similar Bianchi Type VIII and IX Models