Two subsequent cases reached the appeals courts on the Appointments Clause issue after the administrative process played out, and they split on the question.

In Raymond J. Lucia v. S.E.C., involving charges of violations of the Investment Advisors Act of 1940, a three-judge panel of the United States Court of Appeals for the District of Columbia Circuit held that the in-house judges were not “inferior officers” so their hiring did not violate the Constitution. Mr. Lucia and his firm then asked the full court to decide the case — an “en banc” review — but the judges were equally divided on a 5-5 vote on the question, thereby affirming the panel decision.

In the meantime, the United States Court of Appeals for the 10th Circuit in Denver reached the opposite conclusion in Bandimere v. S.E.C., invalidating an order requiring the defendant to disgorge over $600,000 and prohibiting him from associating with securities firms. The appeals court rejected the analysis in the Lucia decision, holding that because the administrative law judge “was not constitutionally appointed, he held his office in violation of the Appointments Clause.”

The S.E.C. asked for en banc review of that decision, but the appeals court denied the request in May. In response, the agency issued an order suspending all administrative cases in which a decision could be reviewed in the 10th Circuit, which covers Colorado, Kansas, New Mexico, Oklahoma, Utah and Wyoming.

That kind of inconsistency in the law demands the Supreme Court resolve the split in how the appeals courts assess whether the S.E.C.’s administrative judges were appointed properly.

The vehicle will most likely be Mr. Lucia’s case, in which he filed a petition in late July with the justices asking them to take up the issue. He has received support for his argument from the United States Chamber of Commerce and Mark Cuban, the owner of the Dallas Mavericks who has been a frequent critic of the agency.

In the petition, Mr. Lucia cites an opinion issued in 2007 by the Office of Legal Counsel in the Justice Department on the scope of the Appointments Clause as support for his position. The opinion asserts when the constitutional requirement for appointment by the president or someone answerable to the chief executive is required: “a position, however labeled, is in fact a federal ‘office’ if (1) it is invested by legal authority with a portion of the sovereign powers of the federal government, and (2) it is ‘continuing.’”