There were no immediate reports of injuries or damage in the capital, Port Vila.
Australia's Emergency Management Office warned the powerful quakes could generate a tsunami, said police spokesman Capt. Arnold Giro.
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"We are moving (coastal) communities to higher ground" on the southern islands, he said. "We have advised the islands to be alert for a possible tsunami."
He said they were still checking on injuries and damage.
A magnitude 7.2 quake hit at 11:40 a.m. local time was located 210 miles southeast of Port Vila and 75 miles south of the small volcanic island of Tanna, police said. It occurred 4.7 miles beneath the earth's surface.
The temblor was followed 28 minutes later by a magnitude 6.0 quake 220 miles southeast of Port Vila and some 85 miles south of Tanna, according to the U.S. Geological Survey.
Police spokesman Capt. Arnold Giro said emergency services were still checking the effects of the quakes in remote islands close to where they were centered.
"We experienced a little bit of movement (in Port Vila) but not as destructive as might be expected," he told The Associated Press.
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