Electronic Journal of Differential Equations, Vol. 2003(2003), No. 72, pp. 1-12. Title: Shigesada-Kawasaki-Teramoto model on higher dimensional domains Authors: Dung Le (Univ. of Texas at San Antonio, USA) Linh Viet Nguyen (National Univ. of Saigon, Vietnam) Toan Trong Nguyen (National Univ. of Saigon, Vietnam) Abstract: We investigate the existence of a global attractor for a class of triangular cross diffusion systems in domains of any dimension. These systems includes the Shigesada-Kawasaki-Teramoto (SKT) model, which arises in population dynamics and has been studied in two dimensional domains. Our results apply to the (SKT) system when the dimension of the domain is at most 5. Submitted June 15, 2003. Published June 27, 2003. Math Subject Classifications: 35K57, 35B65. Key Words: Cross diffusion systems; global attractors.