TITLE: Some models for the Trojan motion AUTHORS: Frederic Gabern and Angel Jorba Departament de Matematica Aplicada i Analisi Universitat de Barcelona Gran Via 585 08007 Barcelona, Spain E-mails: gabern@mat.ub.es, angel@maia.ub.es ABSTRACT: We focus on the dynamics of a small particle near the triangular points of the Sun-Jupiter system. To try to account for the effect of Saturn (and to simulate in a more realistic way the Sun-Jupiter relative motion), we develop specific models based on the numerical computation of periodic and quasi-periodic (with two frequencies) solutions of the planar three body problem Sun-Jupiter-Saturn and write them as perturbations of the Sun-Jupiter RTBP.