A Texas death row inmate may have faked mental illness to avoid execution for the fatal shooting of his ex-girlfriend and her daughter 23 years ago in Houston, a federal appeals court said.

The 5th U.S. Circuit Court of Appeals ruling late Monday agrees with a lower court and moves Gerald Eldridge, 52, a step closer to execution, despite his claim of mental illness.

The U.S. Supreme Court has said mentally ill people can be executed if they have a factual and rational understanding of why they're being punished.

Eldridge was convicted of the January 1993 slayings of his former girlfriend, Cynthia Bogany, 28, and her 9-year-old daughter, Chirissa. Also shot and wounded were Eldridge's then-7-year-old son with Bogany, Terrell and the woman's boyfriend at the time, Wayne Dotson.

Eldridge in 2009 was less than two hours from his scheduled lethal injection in Huntsville when U.S. District Judge Lee Rosenthal halted the punishment. His lawyers had argued Eldridge was too mentally ill to be executed and Rosenthal said the claim needed to be examined.

At a 2013 hearing, Rosenthal heard testimony from four mental health experts — two from Eldridge's lawyers and two from the state — and ruled that while there was evidence of mental illness, there was extensive evidence inconsistent with his claims of incompetence, particularly that he faked symptoms in a behavior known to psychologists as malingering.

Eldridge's lawyer, Lee Wilson, said Tuesday in an email that he had filed a request for a rehearing before the appeals court and would continue to appeal the case.

"Mr. Eldridge is schizophrenic," he said.

Terrell Bogany testified at Eldridge's 1994 trial, describing how his father kicked in the door of their apartment and shot him and how Chirissa, his half-sister asleep on a couch, was shot between the eyes. The boy also described Dotson being shot and seeing his mother run from the apartment with Eldridge in pursuit. Evidence showed Cynthia Bogany was shot outside as she tried to flee to a neighboring apartment.

Records showed Eldridge was sentenced in 1985 to eight years in prison for an earlier shooting where three men were wounded. He was released three years later, then returned to prison in 1990 for beating his son. He was paroled after four months.