MPEJ Volume 2, No.4, 33pp Received: June 19, 1996, Accepted: June 21, 1996 L. H. Eliasson Absolutely Convergent Series Expansions for Quasi Periodic Motions ABSTRACT: CONTENTS. I. INTRODUCTION. * The Hamiltonian problem II. THE CLASSICAL APPROACH TO THE HAMILTONIAN PROBLEM - ABSOLUTELY DIVERGENT SERIES. * The formal solution and its series expansion * "Killing the constants" and the Lindstedt series * Index sets * Description of the coefficients * Convergence and divergence of the formal solution III. SIEGEL'S METHOD. * Siegel's first lemma * Siegel's second lemma * Siegel's third lemma IV. GENERALIZATION OF SIEGEL'S FIRST LEMMA. * Resonances on linear index sets * An equivalence relation on $ad(\gamma)$ * Generalization of Siegel's first lemma - proposition 4 * The basic compensations * Proof of proposition 4 V. GENERALIZATION OF SIEGEL'S THIRD LEMMA. * Resonances on index sets * Generalization of Siegel's third lemma - proposition 5 VI. ABSOLUTELY CONVERGENT SERIES. * Interpretation of the series * "Killing the constants" * Theorem * Other examples