The stars of the TLC show "Sister Wives" say the law is unconstitutional because it prohibits them from living together and criminalizes their private sexual relationships.
Formerly of Lehi, the Browns moved to Nevada in January after police launched a bigamy investigation.
No criminal charges have been filed.
State attorneys say the judge should dismiss the lawsuit. They say the Browns are not likely to be prosecuted.
Oral arguments in the case are set for Friday before U.S. District Judge Clark Waddoups.
