The justices said Monday they will take up the cases from Arizona and Ohio in the fall.
In each case, a death row inmate won an indefinite delay from federal judges based on disputed claims of mental incompetence to understand the proceedings against him and aid in his own defense.
Sean Carter was sentenced to death for raping and killing his adoptive grandmother in 1997. Ernest Valencia Gonzales received a death sentence for a murder in Arizona in 1990.
The cases are Ryan v. Gonzales, 10-930, and Tibbals v. Carter, 11-218.