The U.S. Supreme Court agreed on Monday to hear two death penalty cases brought by black Texas inmates, one claiming racial bias in the criminal justice system and the other focusing on standards for determining whether a defendant is intellectually disabled.

Both cases involve convicted murderers in the state that executes more death row inmates than any other.

The racial bias case involves inmate Duane Buck, 52, and centers on testimony by an expert witness during his trial who said Buck was more likely to be dangerous in the future because he is black. Buck was convicted of the double murder in Houston of his former girlfriend and another man in 1995.

His current lawyers said in court papers that the lawyer who represented Buck during his trial called a clinical psychologist to testify on the likelihood of Buck committing future offenses. The expert testified that Buck was more likely to be dangerous because he is black. Buck's current lawyers said in court papers that "the alleged link between race and future dangerousness has been proven false."

"We are hopeful that the Supreme Court will correct this egregious error, and that Texas will acknowledge Mr. Buck's right to a new sentencing hearing free of racial bias. Justice can only be served in this extraordinary case of racial bias by a new sentencing hearing free of inflammatory, inaccurate stereotypes," Buck's lawyers said in a statement.

They are asking the Supreme Court to reverse a federal appeals court decision in August 2015 that Buck could not pursue his claim that his trial lawyer was ineffective.

The second case involves inmate Bobby Moore, 56, and focuses on how judges should weigh medical evidence of intellectual disability.

Under Supreme Court precedent, people who are intellectually disabled cannot be sentenced to death. His lawyers say Moore has an IQ of 70, and a lower court ruled in his favor. The Texas Court of Criminal Appeals sided with the state last September, and Moore appealed to the U.S. Supreme Court.

The court on Monday initially announced incorrectly that the justices would consider the question of whether the amount of time he has spent on death row awaiting execution since his 1980 conviction violates the U.S. Constitution's ban on cruel and unusual punishment. The court later clarified that the justices will not consider that issue.

Moore was convicted when he was 20 years old of murdering a 70-year-old grocery clerk while committing a robbery. Moore's lawyers noted in court papers that Moore has twice had his execution date set, including one in which a stay was issued less than a day before he was to have been put to death.

For 15 years, he has been held in solitary confinement, the lawyers said.

The Supreme Court's justices have sharply disagreed among themselves over capital punishment, with two of the court's liberals raising concerns that the death penalty amounts to cruel and unusual punishment. The court will hear arguments in the two cases and issue rulings in its next term, which begins in October and ends in June 2017.