TITLE: On the accuracy of Restricted Three-Body Models for the Trojan motion. AUTHORS: Frederic Gabern^(1), Angel Jorba^(1) and Philippe Robutel^(2) (1) gabern@mat.ub.es, angel@maia.ub.es Departament de Matematica Aplicada i Analisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain (2) robutel@imcce.fr Astronomie et Syst\`emes Dynamiques, IMCCE-Observatoire de Paris, 77 Av.~Denfert-Rochereau, 75014 Paris, France. ABSTRACT: In this note we compare the frequencies of the motion of the Trojan asteroids in the Restricted Three-Body Problem (RTBP), the Elliptic Restricted Three-Body Problem (ERTBP) and the Outer Solar System (OSS) model. The RTBP and ERTBP are well-known academic models for the motion of these asteroids, and the OSS is the standard model used for realistic simulations. Our results are based on a systematic frequency analysis of the motion of these asteroids. The main conclusion is that both the RTBP and ERTBP are not very accurate models for the long-term dynamics, although the level of accuracy strongly depends on the selected asteroid.