The Supreme Court began hearing arguments in the seven-year-old case after Dotcom and the others lost several previous court rulings.
But even if the men lose their latest appeal, they have legal options which could keep their case alive in the New Zealand court system and delay any extradition for several more years.
U.S. authorities in 2012 shut down Dotcom's file-sharing website Megaupload and filed charges of conspiracy, racketeering and money laundering. If found guilty, the men could face decades in prison.
Megaupload was once one of the internet's most popular sites. U.S. prosecutors say it raked in at least $175 million, mainly from people using it to illegally download songs, television shows and movies.