By Emanuella Grinberg and Janette Gagnon

CNN

(CNN) -- The state of Arkansas will resume efforts this week 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. Just one execution has been carried out, three are scheduled this week and four are on hold as inmates exhaust their final appeals.

This is where the remaining cases stand:

The legal wranglings

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 sufficiently hear their cases. The 8th Circuit Court of Appeals denied the appeal, and only one 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, though an appeal from one inmate remains up for consideration by the Supreme Court.

Drug makers attempted to intervene. McKesson Corp. tried to get the Arkansas Department of Correction to return a supply of vecuronium bromide, the drug used to paralyze inmates, arguing that 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.

Marcel Wayne Williams: Monday

Williams' execution is scheduled for April 24.

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.

Williams has been transferred to Arkansas' Cummins Unit, where executions are carried out. After the district court denied him relief, he appealed his claims related to lethal injection protocol and ineffective counsel to the 8th Circuit.

Jack Harold Jones: Monday

Jones' execution is scheduled for April 24.

He was convicted in 1996 of rape and murder for the death 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.

Jones was transferred to Cummins.

On Monday, the 8th Circuit denied his request for a stay.

Kenneth Dewayne Williams: Thursday

Williams' execution is scheduled for April 27.

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 lawyers filed a writ for habeas corpus on Friday claiming he is intellectually disabled and thus ineligible for execution. The circuit court has yet to respond.

Jason Farrell McGehee: On hold

McGehee was scheduled for execution on Thursday, April 27, 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 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 his execution date, the governor will have to sign a new death warrant setting a new date.

Bruce Earl Ward: On hold

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 the convenience store where she worked in Little Rock. 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.

Separate from the mental incompetency claim, the Arkansas Supreme Court granted a stay of Ward's execution pending a Supreme Court decision in another case, McWilliams v. Dunn. The case centers on defendants' access to independent mental health experts, a key issue in Ward's case, his lawyers claim. Arguments are scheduled for Monday.

Don William Davis: On hold

Like Ward, Davis' April 17 execution was halted pending a Supreme Court decision in McWilliams v. Dunn, based on similar arguments.

Davis was convicted in 1992 of murdering Jane Daniel during a home invasion and burglary in 1990. Daniel's husband found his wife shot to death in a storeroom.

Ward and Davis share the same lawyer. Scott Braden 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

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.

Ledell Lee: Executed

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.

CNN's Dakin Andone, Jaide Timm-Garcia and Taylar Smith contributed to this report.