Several authors have pointed out the usefulness of shape theory, which was introduced by K.Borsuk in 1968, as a tool in the study of dynamical systems. In particular, Bogatyi and Gutsu [4], Garay [10], Gunther and Segal [11], Hastings [12], Robbin and Salamon [16], Rogers [17] and Tezer [24] have obtained interesting results in dynamical systems using shape-theoretical techniques. One of the authors of the present article has given another connection between shape and topological dynamics [20], based on the approach to shape developed in [18] and [19]. See also [21] for applications of shape theory to the study of uniform attractors. Most of the mentioned papers study properties of flows, although [16] and [24] are devoted to discrete dynamical systems. In particular, a shape Conley index is constructed in [16] for discrete dynamical systems and some shape-theoretical ideas are used in [24] to study properties of topological conjugacy of shifts and homotopical shift equivalence for maps of polyhedra. In the papers [4,10,11,12,20,21] some topological properties of the attractors of flows are studied. For instance, Hastings established in [12] a higher dimensional Poincare-Bendixson theorem, proving the existence of attractors of certain flows in the interior of submanifolds of the Euclidean space and comparing the shape of the attractor with that of the manifold. Other properties studied in the above papers are related to strong cellularity of the global attractors [10] and polyhedral shape of asymptotically stable compacta [4,11,20]. A remarkable fact proved by