Attorneys for Amazon and Elon Musk’s SpaceX argued in a federal appeals court Monday that the National Labor Relations Board’s structure is unconstitutional, advancing a legal fight that may last into the Trump administration — where Musk, the world’s richest person, is expected to oversee cutting costs across the federal government and deleting regulations that he says “do not serve the greater good.”

A panel of three judges at the 5th U.S. Circuit Court of Appeals in New Orleans heard separate oral arguments in the SpaceX and Amazon lawsuits, which the two companies initiated after the labor agency filed complaints against them in disputes about workers’ rights and union organizing.

A ruling in favor of the companies could diminish — or paralyze — the nearly century- old agency, which is tasked with enforcing labor laws and settling labor-related complaints that workers lodge against their employers. The issue may eventually reach the U.S. Supreme Court, which has a conservative majority and has issued rulings curbing the power of government agencies.

SpaceX, Musk’s space technology company, filed its lawsuit against the NLRB in January after the labor agency accused the company of unlawfully firing employees who wrote an open letter critical of Musk and of creating the impression that worker activities were being surveilled.

Among other claims, the company argued in its complaint that agency proceedings deprived it of the right to a trial by a jury.

Amazon’s lawsuit against the NLRB is tied to the company’s objections to a union election that took place at a warehouse in New York City in April 2022. The retail giant has accused the agency of improperly interfering in that election, partly by bringing a lawsuit against the company to reinstate a fired organizer close to when voting began.

The Amazon Labor Union ultimately won the election to represent workers, but Amazon has refused to come to the negotiating table.