Wayne and Mae Wells were murdered Monday night in their Ivy Bend home on Oak Hill Drive, Morgan County Sheriff Jim Petty said at a Tuesday night news conference.
Each victim had been shot in the head.
KMIZ-TV also reported the couple's daughters think their parents probably knew their attacker.
Officials also said sheriff's deputies arrested a teenager Tuesday - but did not say whether that arrest was connected with the murder.
The couple apparently died during a robbery in their home south of Stover.
Their bodies were found by a friend, who stopped by their home about 11 a.m. Tuesday.
Highway Patrol Sgt. Paul Reinsch, the Troop F information officer, said Troop F officers and the Division of Drug and Crime Control were assisting the Morgan County sheriff's investigation.
The fatal victims were identified as Wayne Wells, 80, and Mae Wells, 72. Authorities report the couple had been shot multiple times in their home.
Two people were found dead Tuesday morning in a home on Oak Hill Drive, in Ivy Bend, south of Stover.
The Morgan County Sheriff's Office has said the deaths are being investigated as homicides, and that they would provide more information during an 8 p.m. news conference.
So far, Sheriff Jim Petty and his staff have not issued any news release or other information.
Highway Patrol Sgt. Paul Reinsch, the Troop F information officer, said Troop F officers and the Division of Drug and Crime Control are assisting the Morgan County sheriff's investigation.
Reinsch said the deaths appeared to be caused by a shooting, but he couldn't confirm a cause of death.
He also said: "We don't know when the killings occurred."
KMIZ-TV reported a friend went to the home about 11 a.m. Tuesday and found an elderly woman lying face down, in blood.
That report said law officers were called and found a man lying in a different part of the home.
A neighbor told officials his dog was barking about 6 p.m. Monday.
Reinsch said he could not confirm any details, including the genders or ages of the victims.
"We're still trying to confirm the timeline of when it happened," he said.