RS 02002.030 Self-Employment Rule under the Australian Agreement
Self-employed workers are not covered by Australia's Superannuation Guarantee legislation. As a result, self-employed workers subject only to Australian laws under the agreement are not required to contribute in either country.
Generally, a work activity that is considered to be self-employment under U.S. Social Security law is also considered to be self-employment under Australian law. In certain cases however, a person may be engaged in an activity that is considered self-employment by one country and employment by the other country. For purposes of applying the agreement, any such activity will be subject to the rules for self-employment.
Residents of the United States who are self-employed are subject only to U.S. law regarding Social Security coverage and taxes. U.S. citizens who reside in Australia and are self-employed are exempt from U.S. law.