Pacific Shaken by Strong Quakes
The US-based Pacific Tsunami Warning Center said neither quake was likely to cause a destructive tsunami.
The stronger tremor hit about 500km (310 miles) off the coast of New Zealand, around the uninhabited Auckland Islands.
There were no reports of any damage and its impact had substantially decreased by the time it arrived at the mainland, the BBC's Greg Ward in Auckland says.
The Guam quake, which hit 350km off the coast at 0209 GMT, was given a 7.1 magnitude by the Japan Meteorological Agency.
Officials at the US Geological Survey said it had a magnitude of 6.8.
Its epicentre, some 30km (19 miles) deep, was in the southern part of the Mariana Islands, the Japanese agency said.
There were no reports of injuries or damage on the US territory.
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