A detailed description of an efficient approach to comparison of protein structures is presented. Given the 3-D coordinate data of the structures to be compared, the system automatically identifies every region of structural similarity between the structures without prior knowledge of an initial alignment. The method uses the geometric hashing technique which was originally developed for model-based object recognition problems in the area of computer vision. It exploits a rotationally and translationally invariant representation of rigid objects, resulting in a highly efficient, fully automated tool. The method is independent of the amino acid sequence and, thus, insensitive to insertions, deletions and displacements of equivalent substructures between the molecules being compared. The method described here is general, identifies 'real' 3-D substructures and is not constrained by the order imposed by the primary chain of the amino acids. Typical structure comparison problems are examined and the results of the new method are compared with the published results from previous methods. These results, obtained without using the sequence order of the chains, confirm published structural analogies that use sequence-dependent techniques. Our results also extend previous analogies by detecting geometrically equivalent out-of-sequential-order structural elements which cannot be obtained by current techniques.