The Relationships Register Regulations 2017 (SA) [reg 7] provide a list of laws of other jurisdictions declared to be corresponding laws. A law of another jurisdiction may be declared to be a corresponding law if, under that law, the relationship must be:

If you are in a registered relationship under a corresponding law, you will be taken to be in a registered relationship under South Australian law [s 27] and may apply to the Registrar for a certificate to that effect.

This application must be accompanied by evidence of the identity and age of each of the applicants, and evidence that the relationship between them is a corresponding law registered relationship, as well as the prescribed fee.

See sections 26 and 27 of the Relationships Register Act 2016 (SA).