ASHINGTON, March 2 - The justices of the Supreme Court appeared to wrestle with contradictory impulses on Wednesday as they heard arguments in two cases challenging government displays of the Ten Commandments.

On the one hand, they were searching for a broad principle that could decide not only these disputes, but future ones as well. On the other hand, they appeared powerfully drawn to deciding the two cases on their specific facts, even at the risk of inviting an endless parade of future cases.

Was the 22-acre park surrounding the Texas Capitol, where a Ten Commandments monument sits among 16 other displays, all of them nonreligious, the equivalent of an outdoor museum or sculpture garden? Fine: maybe just such a mixed display might pass constitutional muster, even if a stand-alone Ten Commandments in a future case might prove more troublesome.

Did it matter that the two Kentucky courthouses now seeking to display a framed Ten Commandments surrounded by nine nonreligious historical documents had at first hung unadorned copies of the Commandments and did not add the other documents until after a lawsuit was filed? If so, if that history provided the constitutional taint that led a federal appeals court to order removal of the entire display, then the answer to whether a display without such a history would be acceptable could wait for another day.

By the end of two hours of argument, it was not clear how the justices would resolve the dilemma they created for themselves when, after 25 years of silence on the Ten Commandments, they agreed to decide these two cases. Justice Antonin Scalia, unsurprisingly, expressed a definitive view, consistent with his long-held position in religion cases. He called the Ten Commandments "a symbol of the fact that government derives its authority from God," adding, "That seems to me an appropriate symbol to put on government grounds."

But Justice Sandra Day O'Connor, who may well be in a position to cast the deciding vote, appeared uncertain as she tried out various approaches to resolving the cases on narrow grounds. Referring to the Texas monument, erected in 1961 by the Fraternal Order of Eagles, she wondered aloud whether "at some point" the preservation of an "old object" might itself provide an independent, nonreligious justification for keeping the Ten Commandments on the Capitol grounds.

The justices' visible struggle reflected the fact that the Supreme Court's own precedents provide relatively little guidance on how to tell the difference between religious displays that amount to an unconstitutional "establishment" of religion and those that acknowledge religion in such a minimal or contextual way that the Constitution is not offended, even if some individuals are.

In 1980, the court invalidated a Kentucky law that required the posting of the Ten Commandments in every public school classroom, but no one seemed to suggest that the old case provided an answer to the new ones. In the new cases, one federal appeals court upheld the Texas display even as another struck down the two in Kentucky.

Would it be permissible for the Texas Legislature to post the Ten Commandments, not in a park, but in the halls of the Capitol, Justice O'Connor asked Erwin Chemerinsky, who was representing the Austin man who challenged the display.

No, replied Mr. Chemerinsky, a professor at Duke University Law School, because that would be a sign of government endorsement of religion.

But the Supreme Court itself has upheld the practice of beginning a legislative session with a prayer, Justice O'Connor pointed out.

"It can't be that just because a prayer is permissible, everything becomes permissible," Mr. Chemerinsky replied, adding that a legislature could not mount a large Latin cross on the top of a state capitol.

"It's so hard to draw the line!" Justice O'Connor exclaimed.

Justice Stephen G. Breyer said he had reluctantly and tentatively come to the conclusion that there was no way to decide religious display cases other than by evaluating the divisive nature of the display case by case.

The Ten Commandments are "enormously divisive," Mr. Chemerinsky responded, urging that the court "not ignore social reality." He mentioned the crowds that the arguments themselves drew to the court, as well as the dispute in Alabama two years ago over the display of a large Ten Commandments monument in the courthouse by the state's chief justice at the time, Roy Moore.

Justice Scalia asked whether the marshal's invocation that begins each Supreme Court session, "God save the United States and this honorable court," was not also "divisive, because there are people who don't believe in God."

Mr. Chemerinsky replied that it was important to draw a distinction between "minimal and maximum religious content." The message of the Ten Commandments was deeply religious he said, adding that "all of these are God's commands to his people."

Justice David H. Souter asked whether a tablet containing only the last five commandments, the injunctions against killing, stealing, and so on, might be constitutional because, unlike the first five, they did not necessarily imply religious belief.

That would be a harder case, Mr. Chemerinsky replied, but such a tablet would still be unconstitutional because it would still convey the Ten Commandments' message.

What about a "piece of stone" simply carved with the various "thou shalt nots," Justice Souter asked.

That would be acceptable as a "reflection of law" rather than religion, Mr. Chemerinsky replied.

"Who are you kidding?" Justice Scalia broke in, adding that "everyone knows" that the reference would be to the Ten Commandments.

"Context matters enormously," Mr. Chemerinsky said.

Greg Abbott, the Texas attorney general, described the Ten Commandments as a "recognized symbol of law" and defended the state's display as having the secular purpose of "recognizing historic influences" on the legal system.

The attorney general's argument distressed Justice Scalia.

"You're watering it down to say the only message is a secular message," the justice said. "I can't agree with you. 'Our laws come from God.' If you don't believe it sends that message, you're kidding yourself."

Later, Justice Scalia told Mr. Abbott, "I would consider it a Pyrrhic victory for you to win on the grounds you're arguing."

In both the Texas case, Van Orden v. Perry, No. 03-1500, and the Kentucky case, McCreary County v. American Civil Liberties Union, No. 03-1693, the Bush administration argued on behalf of the displays.

"The Ten Commandments have an undeniable religious significance, but also a secular significance as a code of law and a well-recognized symbol of law," Paul D. Clement, the acting solicitor general, told the justices. He added: "The Establishment Clause should not be interpreted to force the state to send a message of hostility toward religion."

The question was one of degree, Mr. Clement suggested. In answer to a question from Justice Anthony M. Kennedy, he said that Chief Justice Moore in Alabama "probably" crossed the constitutional line when he turned the courthouse rotunda into the equivalent of a "religious sanctuary." Mr. Clement added: "The state can have a permissible acknowledgment of religion, and I don't think in this case the State of Texas has gone too far."

In defending the Kentucky courthouse displays, Mathew D. Staver, a lawyer with Liberty Counsel, a Florida group associated with the Rev. Jerry Falwell, said the appeals court had "ignored the overall context" when it ordered the removal of courthouse displays that contained the Ten Commandments surrounded by the text of nine historic documents, including the Mayflower Compact.

But it was the context that the justices questioned, several dwelling on the original 1999 displays that contained the Ten Commandments alone. The two counties, McCreary and Pulaski, had decided to "switch rather than fight," Mr. Staver said, and should be "rewarded, not punished, for trying to get things right."

But "the courts cannot turn a blind eye to a sham secular purpose," David A. Friedman, general counsel of the American Civil Liberties Union of Kentucky, told the justices.

Mr. Friedman said a "reasonable observer" would know the history and understand the counties' real purpose.