More than six years after his arrest in a dramatic raid, the effort to extradite internet entrepreneur Kim Dotcom will reach New Zealand's second-highest court.

The German-born founder of Megaupload and his three co-accused - Mathias Ortmann, Bran van der Kolk and Finn Botato - were arrested in 2012 and charged with a series of copyright-related offences on behalf of authorities in the United States over their roles in the popular file-sharing website.

Last year, the High Court at Auckland upheld a previous ruling the group were eligible for extradition on charges of racketeering, wire fraud and money laundering, although it found they couldn't be sent to the US on copyright infringement charges alone.

That prompted an immediate appeal and lawyers for both sides will today resume the drawn-out legal battle, this time at the Court of Appeal.

The tech mogul's lawyers say the decision proved the extradition was no longer the "largest criminal copyright case", conflicted with parliament's intent and wasn't consistent with US law.

The Crown itself is also appealing elements of the High Court decision during the proceedings.

The hearing in Wellington is expected to take about two weeks.

The US Federal Bureau of Investigation has led the investigation and claims Megaupload was a criminal conspiracy that earned the men $175 million.

Meanwhile, Dotcom's lawyers last month said they were suing the New Zealand government for billions of dollars in damages, arguing his arrest warrant was invalid.