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The US-based firm, which launched in New Zealand and Australia in 2011, allows businesses to sell online vouchers and deals to subscribers.
Its website now reads that as of today it can no longer offer any new deals.
"If you are a current customer with a deal voucher that has not been redeemed and is still valid, you have until 30th September to use this. If your voucher expires before 30th September, the original expiration date stands.
"Should you be unable to use a valid voucher you can contact Customer Service to request a refund."
In an email to customers Groupon said the decision to close had been made after a "thorough analysis of the New Zealand market".