Attorneys for nine death row inmates want a judge to deem Arkansas' new lethal injection law unconstitutional.
The death row inmates' lawyers filed a motion for summary judgment on Monday.
The inmates also want a judge to declare that the 2013 Method of Execution Act is invalid as applied to them.
The new execution law came about after the state Supreme Court struck down the previous one in 2012, saying that legislators had ceded too much control over execution procedures to correction officials.
Legislators enacted a new law this year that says the state must use a lethal dose of a barbiturate in lethal injections.
Arkansas last executed an inmate in 2005. The state doesn't have any executions scheduled.