(CNN) The state of Arkansas put two men to death on Monday night , resuming efforts to execute death row inmates before its supply of sedatives used in lethal injection expires.

Arkansas Gov. Asa Hutchinson scheduled eight executions in 11 days, the most in the shortest amount of time since capital punishment returned to the United States in the 1970s, creating a race against the clock and a tangled web of legal challenges.

Hutchinson said it was necessary to follow the law and bring closure to victims' families. But with one week left the state is behind schedule. Three executions have been carried out (including the two Monday ); one more is scheduled this week; and four are on hold as inmates exhaust their final appeals.

Here is where the remaining cases stand:

The legal wrangling

Once an execution is scheduled, new legal issues arise, such as clemency appeals and claims of mental illness, impairment or ineffective counsel, among others.

In addition to arguments from their own cases, the Arkansas eight said in a lawsuit the state's clemency board did not have enough time to hear their cases sufficiently. The 8th US Circuit Court of Appeals denied the appeal, and only one inmate received a clemency recommendation.

As more pharmaceutical companies refuse to make drugs available for capital punishment, inmates have brought cruel and unusual punishment claims stemming from revised execution methods. The Arkansas eight filed such a claim, arguing that midazolam -- the drug used to render inmates unconscious in botched executions in other states -- does not reliably prevent a painful death. The Arkansas Supreme Court denied the claim.

Drug companies attempted to intervene. Distributor McKesson Corp . tried to get the Arkansas Department of Correction to return a supply of vecuronium bromide, the drug used to paralyze inmates, arguing it's only supposed to be used for medical purposes. Its lawsuit temporarily suspended executions until the Arkansas Supreme Court overruled a lower court decision that prevented the drug from being used. Two other drug companies, Fresenius Kabi USA and West-Ward Pharmaceuticals, filed a brief in the inmates' lawsuit arguing contracts prohibit their products from being used in executions.

Kenneth Dewayne Williams: Thursday

Kenneth Dewayne Williams

Williams' execution is scheduled for Thursday.

He was convicted of capital murder in 2000 for the death of Cecil Boren, whom he killed after escaping prison while serving a life sentence for the 1998 killing of Dominique Hurd, a University of Arkansas at Pine Bluff cheerleader.

His attorneys filed a writ for habeas corpus claiming he is intellectually disabled and thus ineligible for execution. The federal appeals court has yet to respond.

Jason Farrell McGehee: On hold

Jason Farrell McGehee

McGehee also was set for execution Thursday until the parole board recommended 6-1 to commute his sentence to life without parole.

He was convicted in 1997 of murdering 15-year-old John Melbourne. After Melbourne was caught stealing shoes on McGehee's behalf with a stolen check, the teenager told police about more stolen checks and property at McGehee's home. McGehee and his friends tricked Melbourne into coming back to the house, where they beat him to death "to teach him not to 'snitch.' "

A federal District Court granted a preliminary injunction staying the execution until the Arkansas Parole Board gives 30 days for public comment before sending a final recommendation to the governor, who has final say. Because the 30-day period will expire after McGehee's execution date, the governor will have to sign a new death warrant setting a new date.

Bruce Earl Ward: On hold

Bruce Earl Ward

Ward's April 17 execution was halted to allow litigation on a claim that he's mentally incompetent.

Ward was convicted in 1990 of murdering Rebecca Doss, whose body was found in the men's restroom at a Little Rock convenience store where she worked. Ward was seen in the store's parking lot. He told police he had shared a cup of hot chocolate with Doss and that she gave him the key to the restroom.

Oral arguments in the Alabama case were held Monday before the high court. Separate from the mental incompetency claim, the Arkansas Supreme Court granted a stay of Ward's execution pending a US Supreme Court decision in an Alabama case, McWilliams v. Dunn . The case centers on defendants' access to independent mental health experts, a key issue in Ward's case, his lawyers say.Oral arguments in the Alabama case were held Monday before the high court.

Don William Davis: On hold

Don William Davis

Davis' April 17 execution also was halted pending a Supreme Court decision in the McWilliams case, based on similar arguments.

Davis was convicted in 1992 of murdering Jane Daniel during a home invasion and burglary two years earlier. Daniel's husband found his wife shot to death in a storeroom.

Ward and Davis share the same attorney, Scott Braden. The lawyer said his clients were "denied access to independent mental health experts, even though they clearly demonstrated that mental health issues would be significant factors at their trials."

Stacey Eugene Johnson: On hold

Stacey Eugene Johnson

Johnson's April 20 execution was stayed after the Arkansas Supreme Court ordered a hearing on DNA evidence.

Johnson was convicted in 1994 of murdering Carol Heath, who was beaten, strangled and stabbed in her kitchen while her two children hid in another room.

Lawyers with the Innocence Project say new methods of DNA testing could prove he's innocent.

Jack Harold Jones: Executed

Jack Harold Jones

Jones was executed Monday night.

He was convicted in 1996 in the rape and murder of Mary Phillips. He abducted Phillips and her 11-year-old daughter from an accounting office in 1995 and robbed them at gunpoint. He raped and killed Phillips and beat her daughter, leaving her for dead. She regained consciousness as police photographers took pictures of the crime scene.

Marcel Wayne Williams: Executed

Marcel Wayne Williams

Williams was executed Monday night.

He was convicted in 1997 of murdering Stacy Errickson in November 1994. Williams forced Errickson into her car at gunpoint and made her withdraw money at several ATMs in transactions caught on camera. Her body was found about two weeks later.

Ledell Lee: Executed

Ledell Lee

Lee was executed on April 21, making him the first person to be put to death in Arkansas since 2005. He was convicted in 1995 of murdering Debra Reese, who was strangled and beaten in her home with a tire thumper her husband gave her for protection. Reese's neighbors saw Lee near the house and identified him to police.