Since the Antarctic Treaty was negotiated in 1959, there have been substantial developments in the law of the sea. One of the most significant developments has been the recognition granted to coastal state entitlements to claim a range of offshore maritime areas. Yet, one of the principal aims of the Antarctic Treaty was to eliminate sovereignty disputes between territorial claimants, and the treaty placed limitations on the assertion of new claims. Nevertheless, most Antarctic territorial claimants have asserted some form of Antarctic maritime claim. This article particularly considers Australia's position toward maritime claims offshore the Australian Antarctic Territory (AAT). It reviews the limitations imposed by the Antarctic Treaty, the difficulties in determining baselines in Antarctica, Australia's practice in declaring Antarctic maritime claims, and the potential range of maritime boundaries that Australia may one day have to delimit with neighboring states in the Southern Ocean. © 1995 Taylor & Francis Group, LLC.