Within an hour, Georgia, then Missouri carried out the nation's first executions since a botched lethal injection in Oklahoma in April raised new concerns about capital punishment.

Neither execution had any noticeable complications. Another execution, the third in a 24-hour span, is scheduled Wednesday evening in Florida.

Georgia inmate Marcus Wellons, 59, who was convicted of the 1989 rape and murder of a 15-year-old girl, received a single-drug injection late Tuesday night after the US supreme court denied his late appeals.

His sentence was carried out about an hour before John Winfield, who was convicted of the 1996 killing two women, was executed early Wednesday in Bonne Terre, Missouri.

Nine executions nationwide have been stayed or postponed since late April, when Oklahoma prison officials halted the execution of Clayton Lockett after noting that the lethal injection drugs weren't being administered into his vein properly. Lockett's punishment was halted and he died of a heart attack several minutes later.

"I think after Clayton Lockett's execution, everyone is going to be watching very closely," Fordham University School of Law professor Deborah Denno, a death penalty expert, said of this week's executions.

Georgia, Missouri and Florida all refuse to say where they obtain their drugs, or if they are tested.

Lawyers for Wellons and Winfield had challenged the secretive process used by some states to obtain lethal injection drugs from unidentified, loosely regulated compounding pharmacies.

Georgia and Missouri both use the single drug pentobarbital, a sedative. Florida uses a three-drug combination of midazolam hydrochloride, vecuronium bromide and potassium chloride.

In the Georgia capital case, Wellons was lying still with eyes closed while the drugs were administered at a prison in Jackson. Minutes into the procedure, he took some heavy breaths and blew air out through his lips as if snoring. There was no visible movement minutes later.

It wasn't immediately clear exactly when the drug began flowing, but typically it is within a minute or two after the warden leaves the room. The warden left the room at 11.32pm on Tuesday, 24 minutes before Wellons was pronounced dead at 11.56pm on Tuesday.

In Missouri, Winfield was executed by lethal injection at 12.01am local time and was pronounced dead at 12.10am, a spokesman for the Missouri department of public safety said. The US supreme court had refused late Tuesday to halt his execution, and Missouri governor Jay Nixon denied clemency.

Winfield, 46, took four or five deep breaths as the drug was injected, puffed his cheeks twice and then fell silent, all in a matter of seconds.

Wellons was convicted in the 1989 rape and murder of India Roberts, his 15-year-old neighbor in suburban Atlanta.

Before the execution began, Wellons said he hoped his death could give Roberts' family peace.

"I'd like to apologize to the Roberts family for my crimes and ask for forgiveness," Wellons said.

In Missouri, Winfield had been dating Carmelita Donald on and off for several years and fathered two of her children. Donald began dating another man. One night in 1996, in a jealous rage, Winfield showed up outside Donald's apartment in St Louis County and confronted her, along with two friends of hers.

Winfield shot all three women in the head. Arthea Sanders and Shawnee Murphy died. Donald survived but was blinded.

Winfield declined to make a statement Wednesday.

Florida inmate John Ruthell Henry, who was convicted of killing his estranged wife and her son, is scheduled scheduled to be executed at 6pm on Wednesday night at a prison in Starke, Florida.

The state said it would move ahead with carrying out the death sentence despite claims that Henry, 63, is mentally ill and intellectually disabled. The state claims anyone with an IQ of at least 70 is not mentally disabled; testing has shown Henry's IQ at 78, though his lawyers say it should be re-evaluated.

Henry stabbed his estranged wife, Suzanne Henry, to death a few days before Christmas in 1985, according to court records. Hours later, he killed her five-year-old son from a previous relationship, the records show. Henry had previously pleaded no contest to second-degree murder for fatally stabbing his common-law wife, Patricia Roddy, in 1976, and was on parole when Suzanne Henry and the boy were killed.

Asked Tuesday if he had discussed with the Department of Corrections what happened in Oklahoma and if any changes were needed in Florida, governor Rick Scott said: "I focus on making sure that we do things the right way here."

Florida and Missouri trail only Texas as the most active death penalty states. Texas has carried out seven executions this year. Florida has executed five men, and Missouri has executed five.