Extensive surveys with long range side-scan sonar, as well as an air-gun sub-bottom profiler and a narrow beam echo-sounder, are described for the eastern half of the Mediterranean Sea. The main structural trends are shown in plan view to follow the curve of the Hellenic Outer Ridge (previously known as the Mediterranean Ridge, East Mediterranean Ridge or Mediterranean Rise), and suggest a structural continuation into the Ionian Islands west of Greece. To the west a similar but smaller feature, the Calabrian Outer Ridge (external to the Calabrian Arc) is described. This is partly welded to the Hellenic Outer Ridge along a narrow suture zone. To the east the Hellenic Outer Ridge is shown to merge into the Cyprus Outer Ridge (external to the Cyprus Arc). The Hellenic Outer Ridge is clearly asymmetrical in cross section, with its steeper slope facing towards the interior of its Arc System. Folds and strike faults have been recognized on sonographs, particularly those of the Hellenic Outer Ridge. Cross-faults (possibly strike-slip) are numerous on the northern slope of this Outer Ridge. Cross-faults are especially well developed where the Ridge is narrowest and highest between Crete and North Africa, and where it may have been thickened by thrusting. In general the intensity of deformation decreases southwards across the Hellenic Outer Ridge. Slumping is probably responsible for progressively reducing the height of the relief produced by folding and faulting. The Hellenic, Calabrian and Cyprus Outer Ridges are interpreted as miogeanticlines related to the Plio-Quaternary phase of the continuing southwards outgrowth of the Hellenic, Calabrian and Cyprus Arc Systems. The large and small scale structures are of particular interest because they show the surface relief of some early evolutionary stages of dominantly compressional submarine mountain ranges before they are subject to subaerial erosion or modified by later tectonism. The driving force of the continuing orogeny is seen as resulting from local mantle diapirs spreading outwards from the Tyrrhenian, Aegean and Turkish regions, rather than from a simple closure of the Eastern Mediterranean due to the supposed convergence of the Eurasian and African 'Plates'.