For the small number of Australians who do not fall into the binary categories of male or female, living in a society divided into men and women presents daily challenges.

Sydney resident Norrie, 52, who uses only a first name, was registered male at birth, but as a child began a quest to discover his or her true identity.

"When I was a child I wasn't happy with boy roles and not being able to play with dolls and stuff. I seemed to identify much more with the feminine side of things, patterned myself on my mother," Norrie said.

"I identified I guess as a transsexual in my early 20s. I had friends who were trannies. I went on hormones. I was doing drag shows. So I had sex change and discovered being stuck in one role wasn't really good for me.

"I thought about what gender would I want to be given the option and it's a whole person - it's male and female in some ways and, in other ways, it's neither. Physically I'm neuter like your pet; socially I'm both."

In 2009, Norrie began a journey to be legally recognised as neither male nor female.

Norrie applied to the Registry of Births, Deaths and Marriages to have "hir" identity certificate changed to sex "not specified", and in 2010, became the first person recognised as neither man nor woman, in the eyes of the NSW government.

Norrie prefers the gender-neutral pronouns "hir" instead of his or her, and "zie" instead of he or she.

But four months later the registry wrote to Norrie after receiving legal advice, and said the change had been issued in error and was invalid.

In 2010, Norrie became the first person recognised as neither man nor woman in the eyes of the NSW government. ( ABC News )

"When it happened I couldn't see a way forward. I was just down in a deep dark black hole. It was a strange time," Norrie said.

"In a way it felt like I'd been socially murdered or socially assassinated. The government said they were going to do this thing and had done it and then pulled it out from under me."

Norrie appealed the decision to the Administrative Decisions Tribunal, but the case was dismissed.

So, Norrie went to the New South Wales Supreme Court, and on May 31 this year, won.

"Oh, we'd won after so long. A court had finally said of course sex is just not binary, don't be silly," Norrie said.

"If you're going to specify male or female, I'm not specifically male or female."

Norrie's fight continues as registrar appeals

The matter was sent back to the Administrative Appeals Tribunal to decide on an official sexless designation for Norrie.

But the legal battle continues. The Registrar of Births, Deaths and Marriages has now applied to the High Court for special leave to appeal.

Norrie's solicitor, Emily Christie from DLA Piper, says the Supreme Court's decision is a legal first.

"This is the first time that a court, anywhere in Australia has recognised that somebody can be something other than male or female," Ms Christie said.

"It breaks open this binary idea of sex, this binary idea of gender identity and says that, yes, there are actually some people in this world who don't fit into these two categories and that the law can and should recognise them."

The court's decision only applies to someone like Norrie, who has had sex affirmation surgery, commonly known as sex reassignment surgery, and who chooses to identify as sex non-specific.

However, there are others whose biological sex is not distinctly male or female.

Intersex Victorian pushes for legal recognition

Tony Briffa was mayor of Hobsons Bay in Victoria. ( ABC News )

Councillor Tony Briffa, the former mayor of Hobsons Bay in Victoria, is also pushing for legal recognition.

"People that are intersex like me are a combination of male and female," Tony Briffa said.

"We were just born that way. That's what nature made us and we should be able to be recognised as a combination of male and female if we want to."

Tony Briffa was born with the physical characteristics of both a male and a female, but doctors made the decision the family should raise the baby as a girl and surgically removed Tony's male attributes.

Tony lived as a woman for 30 years.

"I had a wonderful childhood as Antoinette, grew up as a girl, had wonderful experiences as a woman. Then lived a few years as a man to see what that was like and I took some testosterone. That was an interesting experience but that wasn't the full me either.

"I am a combination of male and female. That is the way that nature made me. And there's nothing wrong with that."

"My birth certificate at the moment says blank so it says that I am nothing. I just want a birth certificate that actually reflects what I am and that is a combination of male and female. It's not really too much to ask."

Facing the challenges of everyday life

For people like Tony Briffa, everyday life throws up a number of challenges.

"I went through a body scanner at Sydney Airport and obviously the staff there realised that I wasn't exactly male so I got asked the question 'Excuse me, are you a man or a woman?' And that's a trick question for someone like me.

"I ended up saying, well, I'm a woman because I knew that was going to be the easier option for me if I was going to be searched because I don't have typical male genitalia.

"So I then was searched, unfortunately, by Customs. But incredibly they didn't search my backpack. They just wanted to search my person to work out what I was. And it's all about my sex."

For intersex and gender non-specific people, the fight for legal recognition is far from over.

"Intersex people have larger issues such as the medicalisation that we receive as children in terms of the surgeries, the non-consensual surgeries that are irreversible, that are often done obviously without our consent or with regard for our future needs, so that's a bigger issue for us.

"And things like marriage. When John Howard changed the Marriage Act to specify that marriage is between a man and a woman, what the hell does that mean for someone like me?"