We show that a class of reaction diffusion systems on RN generates an asymptotically compact semiflow on the Banach space of bounded uniformly continuous functions. If such a semiflow is dissipative, then a unique, non-empty, compact minimal attractor is known to exist. We apply this abstract result to obtain the existence of the compact minimal attractor for reaction diffusion systems on RN that contain appropriate weight functions. We also state conditions, which guarantee that the attractor has finite Hausdorff-dimension. © 1996 Academic Press, Inc.