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 is expected to oversee bureaucratic cost-cutting.

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 immensely diminish – or paralyze - the nearly century-old agency, which is tasked with enforcing labor laws and settling labor-related complaints 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,

The three appellate judges who heard Monday's arguments questioned the legal maneuvering by Amazon and SpaceX to get their cases to the 5th Circuit, where jurists nominated by Republican presidents dominate the appeals court.

A lawyer for the NLRB emphasized during the hearing that both companies filed their appeals after lower courts did not give rulings by requested deadlines.

Michael E. Kenneally, an attorney for SpaceX, retorted that the government was “relying so much on the procedural objections” because of the alleged weakness of its legal argument, a claim that elicited some pushback from the panel.

“That sounds to me like the argument ‘procedure doesn’t matter if I win on the merits,’” Judge James E. Graves Jr., an appointee of former President Barack Obama, said.

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 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.

Musk, the world’s richest person, has become more influential in the past few months after pumping an estimated $200 million through his political action committee to help elect Donald Trump as president.

After he was elected, Trump tapped Musk and former GOP presidential candidate Vivek Ramaswamy to lead a new efficiency commission focused on cutting costs across the federal government. Musk has said the new administration will have a “mandate to delete the mountain of choking regulations that do not serve the greater good.”