Taiwan has rejected same-sex marriages, in a blow to the island's reputation as a rights trailblazer in Asia.
A rally in support of same-sex marriage near the Presidential Office in Taipei on 18 November. Photo: AFP
The results in referendums come despite a high court ruling in March 2017 in favour of such unions.
The court also gave parliament two years to amend laws or pass new ones. It is unclear how Saturday's voting will affect legislation.
Meanwhile, President Tsai Ing-wen quit as leader of Taiwan's governing party after defeats in local elections.
Her pro-independence Democratic Progressive Party (DPP) lost more than half of the 13 cities and counties it won in 2014.
Taiwan's relations with China have deteriorated since Ms Tsai came to power in 2016.
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.
What were voters asked about same-sex marriage?
The marriage issue was actually the subject of three separate referendums on Saturday, which were put forward by rival camps.
Conservative groups asked whether the legislation - defining marriage as a union between a man and a woman in Taiwan's Civil Code - should remain unchanged, while LGBT activists asked for the marriage law to be amended to include same-sex couples.
Results show voters backed the conservative "pro-family" groups.
The government earlier said Saturday's referendums would not affect it bringing in the changes required by the court ruling. The authorities are now expected to pass a special law, without amending the Civil Code.
But campaigners fear the eventual legislation will be weaker.
One possible outcome could be that gay couples are given legal protection - but not allowed to get married, correspondents say.
What about President Tsai's move?
At a news conference, she admitted her party had suffered a series of defeats in key local elections.
"Our efforts weren't enough and we let down all our supporters," the president said.
Meanwhile the China-friendly former ruling party KMT made a dramatic comeback, winning 15 of the 22 cities and counties in Taiwan.
Nearly 21,000 candidates were vying for 11,000 elected positions, from mayors to city councillors and township chiefs.
- BBC