The Valentine Day lawsuits to be filed in Tokyo and in other courts around the country on Thursday argued that the law violates same-sex couples' constitutional rights to equality.
They want the government to follow the example of many other nations in guaranteeing marital freedom.
Ten Japanese municipalities have enacted "partnership" ordinances for same-sex couples to make it easier for them to rent apartments together, among other things, but they are not legally binding.
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Many LGBT people hide their sexuality, fearing prejudice at home, school or work. The obstacles are worse for transgender people, who face extra difficulties including a requirement they be sterilized to marry someone of the same birth sex.