The US Supreme Court has begun hearing arguments about whether it is legal for the Ten Commandments to be displayed on government property.
The hearing is focused on buildings in Texas and Kentucky.
The judges must decide whether the monuments are merely a tribute to US history or an unconstitutional break with the church-state separation.
Observers say the hearing has sparked a vigorous debate between Christian conservatives and secularists.
A lawyer opposed to the displays argued before the court that as so many of the Commandments refer to God, they promote religion.
But supporters of the monuments maintain that removing them would create huge challenges in dealing with thousands of other religious symbols that appear in public property.
Justice Anthony Kennedy suggested there may be an "obsessive concern" over any mention of religion.
Another judge, Stephen Breyer, said that although the US is a highly religious country, "we are also committed to secularism".
The Supreme Court last ruled on the issue in 1980, when it struck down a Kentucky law that required schools to put up copies of the Ten Commandments.
But US lower courts have recently made a number of contradictory rulings on the issue.
A ruling is not expected until June.
Two cases
In one case, the justices are hearing about a large granite monument inscribed with the Ten Commandments on the Texas Capitol grounds.
Van Orden says the Texan statue breaches the constitution
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This case has been brought by Thomas Van Orden, a homeless and unemployed lawyer.
He is appealing after losing a lawsuit to have the 2m (6ft) red granite monument removed from the grounds.
He says the statue breaches the constitutional separation of church and state.
The constitution's First Amendment says the two should be kept apart.
In the other case, the judges are considering whether a Kentucky court wrongly barred the posting of framed copies of the Ten Commandments at two county courthouses.