The first ever lawsuit challenging Korea’s ban on same-sex marriage started on Monday.

The lawsuit, which was heard behind closed doors in the Seoul Western District Court, hopes to build on the momentum of the US Supreme Court’s same-sex marriage ruling two weeks ago.

Filed by Kim-Jho Gwang-soo, a film director and LGBT activist and Kim Seung-hwan, a head of the Rainbow Factory production company, the lawsuit is the first of its kind to be filed in Korea.

The couple were the first to hold a public wedding in the Asian nation, where same-sex marriage remains a taboo.

Knowing their application would be rejected, after a public wedding ceremony in September 2013, the couple submitted their marriage licences to the Seodaemun District Office.

According to the office, the constitution of Korea only recognises opposite-sex couple.

The couple called the rejection of their application “utterly groundless”, and challenged the counrt to recognise same-sex marriage.

They walked into the court hand-in-hand on Monday, wearing rainbow badges.

They said Monday was “a crucial day” for Korea.

However the country may have quite a way to go. Its Military Criminal Act makes homosexuality illegal, and those found guilty can face up to two years in prison.