Study of a massless electrons approximation model issued from plasma physics and quasineutrality Sylvie Fabre (CMAP - Ecole Polytechnique) Abstract: In this paper, we study the existence and uniqueness of solutions of Poisson's equation in lRN coupled with Boltzmann relation which gives a particular expression of the electronic density. We consider also the case where the ionic density vanishes. At last, an asymptotic analysis yields a proof of the quasineutrality hypothesis of this model where the Debye length can be neglected in comparison of the size of the system. Resume Nous presentons ici une etude de l'existence et unicite de solutions de l'equation de Poisson dans lRN co uplee àa la relation de Boltzmann qui donne une expression p articuliere de la densite electronique. Le cas d'une densite ion ique nulle est aussi examine. Enfin, une analyse asymptotique permet de prouver la validite de l'hypothese de quasineutralite de ce modele oùu la longueur de Debye est negligeable devant la ta ille du systeme. The whole paper is available as a compressed Postscript file by internet procedure FTP anonymous on host barbes.polytechnique.fr ( 129.104.4.100) in the directory pub/RI/1995 under the name fabre_317.mar.ps.gz or by Xmosaic or any other www client via the CMAP www server "http://blanche.polytechnique.fr/"