By Charlotte Greenfield

WELLINGTON (Reuters) - A New Zealand judge gave permission on Tuesday for the hearing of German tech entrepreneur Kim Dotcom's appeal against his extradition to be streamed on YouTube, making it the country's first court case to be broadcast on the Internet.

The six-week hearing opened in Auckland this week, nine months after a lower court ruled Kim Dotcom could be sent to the United States to face copyright infringement and money-laundering charges over the filesharing website Megaupload.

The case has been closely watched by the media industry and developers in the file-sharing business for signs of how far the United States is willing to go to protect U.S. copyright holders.

"It's very important that the entire world gets to see the courtroom," said Dotcom's lawyer, Ira Rothken. "The Internet isn't run by any one nation, so we thought the solution itself would come from the Internet."

Dotcom was arranging for a videographer to start recording the proceedings from Wednesday, the lawyer added. They will appear on Youtube with a 20-minute time lag to ensure removal of any material suppressed by the court.

The judge ordered the stream to be taken down at the end of the hearing.

New Zealand government prosecutors, who are representing the United States, had argued against the live streaming.

The government law office did not immediately respond to a request for comment but a spokeswoman on Monday said it was not appropriate to comment while the matter was before the courts.

Media reported that the lawyers had argued on behalf of the U.S. that live streaming could be prejudicial, as submissions made in the New Zealand court could be inadmissible in a future trial in the United States.

Legal experts believe the live streaming of an entire hearing will be a first in New Zealand, although domestic media sometimes film brief snatches of courtroom argument.

"The New Zealand judiciary have been very cautious about letting cameras into the courtroom," said Bill Hodge, a criminal law professor at Auckland University, adding that the exceptional nature of the case could have contributed to the decision.

Years of legal wrangling followed Dotcom's arrest during a raid by New Zealand police working in cooperation with the Federal Bureau of Investigation in 2012.

It later emerged that the Government Communications Security Bureau had illegally spied on him before the raid.

U.S. authorities say Dotcom and three co-accused Megaupload executives cost film studios and record companies more than $500 million and generated more than $175 million by encouraging paying users to store and share copyrighted material.

(Reporting by Charlotte Greenfield; Editing by Clarence Fernandez)