One of those challenges was instigated by Nebraska abortion provider, Doctor Leroy Carhart.
It was a legal challenge by Carhart that led the U.S. Supreme Court to overturn Nebraska's so-called partial-birth abortion ban in 2000.
Carhart's most recent challenge was filed by the Center for Reproductive Rights.
The other challenges to the federal ban were filed by Planned Parenthood and the American Civil Liberties Union.
The federal act bars a procedure referred to by critics as partial birth abortion and by medical organizations as "intact dilation and extraction."
During the procedure, a fetus' legs and torso are pulled from the uterus and its skull is punctured.
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