The tickets never came.
Many other complaints about the company have been posted on the internet, and a blog catalogues warnings over its alleged scams.
Police believe the company is now turning its attention to the London Olympics.
London Detective Superintendent Nick Downing said New Zealanders who had made purchases from Euroteam were in danger of not making it into the games.
"I am seriously concerned that anyone who has bought Olympic or Paralympic tickets will now not receive them."
"There is an ongoing investigation by the Norwegian Police into the wider activity of this company, and we know that the company have stated that they have not sourced all of the Olympic and Paralympic tickets that they have sold."
Anyone who had bought tickets from Euroteam should attempt to contact the company directly and seek advice from the point of payment provider, police said.
Sites under suspicion:
www.euroteam.net
www.tixnet.com
www.olympicticket.info
www.euroteam.info
www.euroteamtickets.com
www.2012tickets.org
www.londonsummergames.net
www.londonsummergames.org
www.euroteam.travel
www.worldticketservice.net