A federal court of appeal weighs up whether Robert Mueller's decision to lead the Russia investigation was constitutional.
Thursday was the question of whether deputy Attorney General Rod Rosenstein had the authority to appoint Mueller.
The office of the special council says yes. But lawyers for a former assistant to the old Trump confidant Roger Stone say no. The assistant, Andrew Miller, brought the case because he did not want to testify before a big jury as part of Mueller's research on whether Donald Trump's Republican campaign coordinated with Russia in 2016.
Mueller concentrates on the connection of Stone with WikiLeaks. US intelligence officials have concluded that Russian agents were the source of harmful information about Democrat Hillary Clinton WikiLeaks released during its 2016 presidential campaign against Trump.
Stone has denied every mistake.