TITLE: KAM Theory Without Action-Angle Coordinates AUTHORS: Alejandra Gonzalez(1), Angel Jorba(1), Rafael de la Llave(2) and Jordi Villanueva(3) (1) Departament de Matematica Aplicada i Analisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona (Spain) E-mails: gonzalez@maia.ub.es, angel@maia.ub.es (2) Department of Mathematics, University of Texas at Austin, Austin, TX 78712 (USA). E-mail: llave@math.utexas.edu (3) Dept. de Matematica Aplicada I (ETSEIB), Universitat Politecnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain). E-mail: jordi@tere.upc.es ABSTRACT: The classical KAM methods, strongly supported on the use of canonical transformations in the action-angle context, are not efficient to be applied to a wide range of systems in which the Hamiltonian is known (for instance) written in Cartesian coordinates. In this communication we present some ideas to deal with KAM theory using ``parameterizations'' instead of ``transformations'' and ``graphs'', which we think is an efficient way to work with a more general class of Hamiltonian systems than the classical methods (in particular, for systems motivated by real world problems). With the present approach, we can extend several well-known results of KAM theory to these systems, even when the classical statements are difficult to be applied.