Arkansas will hold two executions on the same day, if two inmates are put to death as planned on April 24.
Lawyers for inmates Jack Jones and Marcel Williams are seeking stays of execution on grounds of poor health.
Arkansas initially planned to execute 8 inmates over 11 days before a drug used in executions could expire.
Last week, Ledell Lee was put to death in Arkansas’ first execution since 2005.
Another inmate, Kenneth Williams, is due to be put to death on April 27, though his lawyers say he is intellectually disabled.
The remaining four of the eight planned executions have been placed on hold by court order.
However, Arkansas’ top prosecutor has vowed to overcome legal obstacles and haul the condemned back to the death chamber.
The last time a state executed two inmates on the same day was in 2000 in Texas.
Both inmates due to be put to death on April 24 have admitted they are guilty.
Jack Jones was convicted in 1996 of raping and strangling Mary Phillips and attempting to murder her 11-year-old daughter.
He was also convicted of rape and murder in Florida.
Marcel Williams was sentenced to death in 1997 for kidnapping, raping and murdering Stacy Errickson.
He also abducted and raped two other women.
Jack Jones is scheduled to be put to death at 19:00 local time at Cummins Unit prison, while Marcel Williams is due up next in the chamber at 20:15.
Their application for a stay of execution to the 8th Circuit Court of Appeals on April 23 is expected to be among a last-minute flurry of such motions.
Jack Jones and Marcel Williams argue that obesity and related conditions mean midazolam, a sedative used in the three-drug cocktail for lethal injections, may not work on them.
Attorneys for Jack Jones say he could suffer from a “torturous death” because he may be resistant to midazolam.
They say the inmate is already taking high doses of two other drugs for a host of maladies, including diabetes, high blood pressure and neuropathy.
Lawyers for Marcel Williams say it may be difficult to find a vein on their client for the lethal injection because he weighs 400lb.
On April 21, a federal judge in Little Rock, Arkansas, rejected a challenge on health grounds from Marcel Williams and Jack Jones.
A lawsuit from the company that makes one of the execution drugs has been among a wave of legal challenges to the state’s unprecedented execution schedule.
Arkansas Supreme Court last week threw out the manufacturer’s lawsuit, which had argued that the state did not make clear if wished to use the supplies for executions.