Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)The main goal of this paper is to study the existence and nonexistence of coexistence states for a Lotka-Volterra symbiotic model with cross-diffusion. We use mainly bifurcation methods and a priori bounds to give sufficient conditions in terms of the data of the problem for the existence of positive solutions. We also analyze the profiles of the positive solutions when the cross-diffusion parameter goes to infinity. (c) 2008 Published by Elsevier Inc.246521312149MEC [MTM2006-07932]Proyecto SantanderConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)MEC [MTM2006-07932]