The Supreme Court will hear appeals from two African-American death-row inmates in Texas, including one who argued his sentence was based on his race.

The justices on Monday said they will review death sentences for inmates Bobby Moore and Duane Buck. Neither case poses a broad challenge to the death penalty.

Moore was sentenced to death more than 35 years ago and says he is ineligible to be executed because he is intellectually disabled.

A jury voted to sentence Buck to death after a defense expert testified that black people were more likely to commit violence. Buck's lawyers have fought for years to win a new sentencing hearing.

Buck came close to being executed in 2001, before the justices stepped in with a last-minute reprieve.

But the court later denied a full-blown review of Buck's case in 2014.

This time around, the appeal focuses on a claim that Buck's legal representation was constitutionally deficient.

He was convicted of capital murder and sent to death row for the slaying of his ex-girlfriend and a man at her Houston apartment in July 1995.  During the punishment phase of Buck's 1997 trial, psychologist Walter Quijano testified under cross-examination by a Harris County prosecutor that black people were more likely to commit violence.

Quijano, called as a defense witness, had testified earlier that Buck's personality and the nature of his crime, committed during rage, indicated he would be less of a future danger.

Buck's case was among six in 2000 that then-Texas Attorney General John Cornyn, now a Republican U.S. senator, said needed to be reopened because of racially charged statements made during the trial sentencing phase.

In the other five cases, new punishment hearings were held and each convict again was sentenced to death.

The attorney general's office has said Buck's case was factually and legally different from the five others and that Buck's trial lawyers first elicited the testimony from the psychologist. They also said the racial reference was a small part of larger testimony about prison populations.

The cases, Moore v. Texas, 15-797, and Buck v. Stephens, 15-8049, will be argued in the fall.