Yesterday, Australia had its first legal same-sex marriages. And their stories are beautiful.

Wedding bells have rung for some same-sex couples this weekend, after special dispensation was given for them to marry without the required 30-day waiting period.

Lauren Price, 31, and Amy Laker, 29, exchanged vows in Camden in Sydney’s south-west on Saturday after getting the waiver because their families were travelling from Wales to attend what was to have been their commitment ceremony.

The wedding took place in front of 65 guests, and the couple were joined by their dog.

Amy and Elise McDonald, likewise were given a financial exemption to marry in Melbourne's Carlton Gardens with their family flying in from overseas.

Yesterday, their 60 guests were surprised and overjoyed to witness the legal marriage.

Speaking to the Herald Sun, the couple said they had planned a commitment ceremony, before realising they could be eligible for an exemption from Births, Deaths and Marriages, since Elise's parents were flying from Asia, and other siblings from the United Arab Emirates.

"We were always going to have a ceremony but to have it legalised is very special," Elise told the Herald Sun.

West Australian couple, Anne Sedgwick and Lyn Hawkins, will wed on Sunday after being together for 40 years.

They were given dispensation as Ms Hawkins, 85, is in the final stages of her battle against ovarian cancer.

Listen: Mia Freedman, Holly Wainwright and Jessie Stephens discuss the moment Australia voted yes to same-sex marriage. Post continues after audio.

"Anne has been very supportive through all this and marrying her, it's Anne's way of saying 'let's finally do this'," Ms Hawkins told Perth Now.

On Monday, Cas Willow, 53, and Heather Richards, 56, will marry at the Peter MacCallum Cancer Centre, where Ms Willow is receiving treatment for breast cancer which has spread to her brain.

The couple, who have been together for 17 years, says marriage will make their last precious few weeks or days together "complete".

"It means our relationship won't just be tolerated, it will be accepted," Ms Richards told AAP. “I don’t even know if I’ll make it to Christmas, let alone January 9, so they allowed us to get married early."

The couple only got engaged after the new law passed on December 9.

January 9 was expected to be the first day of same-sex weddings after the minting of fresh laws requiring couples give four weeks notice, but some couples have been given permission to tie the knot sooner.

Melbourne couple Megan Stapleton and Stephanie Dybal have also been given the green light to wed before January 9.

The couple had planned a non-binding wedding for December 21 and were granted approval to go ahead with a legal wedding on the same date.

With AAP.