The governing Democratic Progressive Party; the opposition Nationalist Party, or Kuomintang; and the smaller New Power Party have each proposed same-sex marriage bills. As of Friday, the bills were in the hands of a Legislative Yuan judiciary committee.

Taiwan has considered marriage equality before. Hsiao Bi-khim, a legislator from the Democratic Progressive Party, submitted a same-sex marriage bill in 2005 that was blocked outright. In 2013, a bill reached the committee review stage but stalled. Now, Ms. Hsiao said, things are different.

“We have a much better chance this time around,” she said. If a bill comes to a vote in the Legislative Yuan, it will need the support of at least 57 of the body’s 113 lawmakers for passage. So far, Ms. Hsiao said, the bills have collectively received backing from 56 legislators.

All of the bills would legalize same-sex marriage and permit gay couples to adopt, said Yu Mei-nu, a legislator who submitted the Democratic Progressive Party’s proposal. The author of the Kuomintang bill, Hsu Yu-jen, also co-signed the Democratic Progressive Party draft, highlighting the momentum that marriage equality has gathered in both major parties, although some members of each party oppose it.

Public support for legalizing same-sex unions is robust, Ms. Yu said. She noted the large turnout last month for the 14th L.G.B.T. Pride Parade in Taipei, which attracted about 80,000 participants from Taiwan and around Asia.

Ms. Yu said legalization had a good chance of passing in Taiwan’s next legislative session, from February through May. But if the proposal fails then, its chances in the sessions that follow — ahead of the local elections in November 2018 — could be lower, she said, as the issue remains controversial.

“This is a golden opportunity,” Ms. Yu said. “But the opposition is strong.”

She noted that legislators who had initially signed on to the 2013 bill withdrew their support after being pressured by groups opposed to same-sex marriage.