How do we respond to indigenous and Muslim women living (including some other cultures) in polygamous relationships, according to their traditional, cultural and religious practices?
What are the social and legal developments in Australia. The Family Court has jurisdiction with respect to void Australian marriages, including marriages void as polygamous under s 23(1)(a).
Well we can refer to the section 94 of the Marriage Act 1961 in relation to polygamy. We need to refer to Part VA of the Marriage Act in relation to validity of foreign marriage under Australian law.
Polygynous Aboriginal Marriages. To the extent that traditional marriage is polygynous (as it is in a minority of cases), recognition might be seen by some as an affront to the established view of marriage in Australian society. So the case Ghazel and Anor  FamCAFC 31 (4 March 2016) the Full Court (Finn, May & Austin JJ) is an interesting decision.
As per The Full Court it may be the case that a marriage solemnised in Iran that was potentially (although not actually) polygamous under the Act is valid – Act’s definition of marriage does not exclude recognition of such a marriage (but would exclude a marriage where a party was already married)
A person who marries another person, knowing that the previous marriage is still subsisting, commits an offence of bigamy under section 94 of the Marriage Act 1961 . This carries a maximum penalty of five years in prison.So the short answer would be that Polygamy is not permitted in Australia.
In Ghazel and Anor  FamCAFC 31 (4 March 2016) the Full Court (Finn, May & Austin JJ) heard the mother’s appeal against Hogan J’s dismissal of her application for a declaration of validity of the parties’ Iranian marriage recognised as valid under s 88D of the Marriage Act 1961 (Cth). The wife (who was born in England) married the husband in Iran in 1981. Hogan J said that the law of that country “permitted a husband subject to certain conditions to take up to three additional wives.