TITLE: ALGEBRAIC CHARACTERIZATION OF AFFINE STRUCTURE ON JET AND WEIL BUNDLES AUTHOR: David Blazquez-Sanz Departament de Matematica Aplicada i Analisi Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain ABSTRACT: We characterize natural transformation between Weil Bundles that are endowed with a canonical affine structure and show several cases. Those transformations are often passed down to Jet Spaces, and we characterize the cases in which the affine structure is also passed down. We prove that the classical situation is an example and give some practical generalization. Key Words: Jet, Weil Bundle, Affine Structure MSJ: 58A20, 58A32 E-MAIL: david@maia.ub.es