Currently, the Council of State must approve any changes to the way North Carolina executes inmates on death row. Attorneys for the Council of State say that judge didn't have the jurisdiction to make the order.
A Superior Court judge later sided with the council.
However, lawyers for the five condemned inmates say the council needed to hear from prisoners' advocates before signing off on any capital punishment changes.
On Monday, the justices heard details of those changes and procedural adjustments dating back to the late 1990s.
"At the same time that the General Assembly did this, they also abolished lethal gas as a method of execuion, and said that lethal injection would be the sole method of execution in the constant march toward a more humane, methods that are thought to be more humane," inmates' lawyer David Weiss said.
If the Supreme Court agrees, the case will go back to a lower court for review.