CONCORD, NH — Two lawsuits involving transgender girl athletes — one challenging a state ban in schools and the other the right to protest their participation on girls’ teams — face federal court hearings in New Hampshire on Thursday.

The first case involves two transgender teenage girls, one who played soccer on the girls’ team last fall and the other who plans to participate on the track team this winter.

A federal judge ruled earlier this year that teenagers can try out and play on girls’ school sports teams as they seek to overturn the Fairness in Women’s Sports Act on behalf of all transgender people in New Hampshire.

The law, signed by Gov. Chris Sununu in July, bans transgender students in grades 5 through 12 from teams that conform to their gender identity. It requires schools to designate all teams as either girls, boys or coed, with eligibility determined based on students’ birth certificates “or other evidence.”

Sununu had said it “ensures fairness and safety in women’s sports by maintaining integrity and competitive balance in athletic contests.” About half of the states have taken similar measures.

In the second case Thursday, a judge is expected to hear from Bow school district officials defending their decision to bar parents from wearing pink armbands emblazoned with “XX” — representing the female chromosomes — at a high school girls’ soccer game in September. The parents sued the district in September.

Parker Tirrell, one of the transgender girls who challenged the state’s ban on participation, played on the opposing team that day.

The district issued a no-trespass ban that banned two parents from school grounds because they were wearing the bracelets. These orders have since expired.

The judge is also expected to hear from the parents, who say their First Amendment rights were violated. They have sought a court order against the school district.

“Although the fall football season has ended, the plaintiffs intend to continue wearing their armbands at other schools outside of school events — such as swim meets and cross country meets — this school year and in future school years,” the parents said in a court filing.

School district officials said they acted appropriately.

The district “properly exercised its duty to protect Parker Tirrell from intimidation and harassment during the game,” a court document states.

It also said it issued reasonable sanctions” against the two parents “for conduct they knew violated the school’s policy on sporting events.”