Taiwan is voting in a referendum on whether to become the first place in Asia to legalise gay marriage.
The top court ruled in favour of same-sex marriage, giving parliament two years to amend laws or pass new ones.
But surveys last week suggest the country will vote against the change.
The issue is one of 10 voters are being asked to consider, including one inflaming tensions with China: how they want to be called at the 2020 Tokyo Olympics, Taiwan or Chinese Taipei.
Currently, Taiwan competes as Chinese Taipei, the name agreed with China in the 1980s.
This is because Taiwan's status is sensitive. The island has been self-ruling since 1949 but China regards it as a breakaway province it will reunite with one day.
The referendums are running alongside local elections. Polls close at 16:00 local time (08:00 GMT), with the first results expected later on Saturday.
Questions
The issue is actually the subject of two separate referendums on Saturday, which have been put forward by rival groups.
Conservative groups have asked whether marriage should be legally defined as between a man and a woman, while LGBT activists have put forward one for equal marriage rights.
The two sides have also put other issues to voters, including rival questions on education around LGBT issues in schools.
According to a survey carried out by the Taiwan Public Opinions Foundation, 77% of respondents believe marriage should be legally defined as between a man and a woman.
How much does the vote matter?
The government has said the vote will not affect it bringing in the changes required by the court ruling more than 18 months ago.
But campaigners fear it will mean the eventual legislation will be weaker.
"We hope that love and equality will win," Suki Chung, East Asia campaigner at human rights group Amnesty International told news agency AFP.
"However, if the opposite happens then the government must not use the result as cover to water down same-sex marriage proposals."
What do the local elections mean for the ruling party?
Nearly 21,000 candidates are vying for 11,000 elected positions, from mayors to city councillors and township chiefs.
Looming over the elections is Taiwan's fraught relationship with China, the BBC's Cindy Sui reports from Taipei.
Since
, relations have deteriorated.
Beijing has refused to deal with her because she does not recognise an agreement reached between the two sides in 1992 that both sides are part of one China.
And that has heightened military tensions, fuelled a loss of Taiwan's diplomatic allies and hurt the economy, our correspondent says.