In one case, a Richland County judge displayed the commandments in his courtroom. In the other, the commandments were displayed in front of Adams County school buildings.
The 6th U.S. Circuit Court of Appeals in Cincinnati said both were illegal.
The Supreme Court sometimes holds private conferences in cases similar to ones in which justices make a ruling. Justices were expected to consider the Ohio cases Monday afternoon, hours after their specific rulings involving challenges from Texas and Kentucky.
In those, the court upheld the constitutionality of displaying the Ten Commandments on government land, but only in some circumstances. A ruling on the Ohio challenges could be released Tuesday.
"The most we can hope for is they vacate those opinions and send them back to the 6th Circuit," said Frank Manion, the lawyer who represented the American Center for Law and Justice in its support of the displays.
John Durkalski, spokesman for the American Civil Liberties Union of Ohio, which opposed the displays, said the state ACLU had no comment on the Monday rulings or the pending Ohio cases.
The Supreme Court, in two 5-4 decisions, upheld the constitutionality of displaying the Ten Commandments on government land, but drew the line on certain renderings inside courthouses.
The justices said the displays are not inherently unconstitutional. But each exhibit demands scrutiny to determine whether it goes too far in amounting to a governmental promotion of religion.
U.S. District Judge Kathleen O'Malley ruled in June 2002 that Richland County Common Pleas Judge James DeWeese violated the Constitution by displaying a framed poster of the Ten Commandments in his courtroom.
That same month, U.S. Magistrate Timothy Hogan ruled that the 800-pound stone monuments inscribed with the commandments must be removed from in front of four high schools of the Adams County/Ohio Valley school district.
Separate three-judge panels of the 6th Circuit court upheld both rulings.