American Samoa could be in the direct path of Cyclone Olaf, which is packing winds of up to 250km/h (155 mph), meteorologists have warned.
Cyclone Olaf is heading across the South Pacific
Olaf appears to have spared much of nearby Samoa, hitting the island of Savai'i but missing the capital Apia.
Meanwhile another cyclone, Nancy, skirted most of the Cook Islands, causing relatively minor damage on the islands of Rarotonga and Aitutaki.
Nancy has now weakened and is not expected to cause much further damage.
There are still fears, however, that Cyclone Olaf could present a serious threat to American Samoa.
According to meteorologists, Olaf has now strengthened to a Category Five "super cyclone", the most powerful on the scale.
Forecaster Oliver Druce told the Australian news agency AAP that it was "about as big as a cyclone can get".
"American Samoa ... could be in the firing line for the most intense part of the cyclone," Mr Druce added. "It only takes 30km between a direct hit and a miss so it's all sort of touch and go."
Residents in American Samoa, which has a population of about 60,000, have boarded up homes, businesses and churches in preparation for the cyclone.
Giant waves are expected to cause flooding in low-lying areas, the territory's National Weather Service said.
Governor Togiola Tulafono has already declared a state of emergency.
"We are anticipating extensive infrastructure damage and limited communications capability in the aftermath of this category five storm," Mr Tulafono said in a statement to President George W Bush.
Cyclone Olaf has now passed Samoa, after causing some damage, but not as much as experts had feared.
"It's off the capital now, causing quite a lot of tidal damage, bringing down power lines and stuff," said Kevin Vang of the Australian-Pacific Center for Emergency and Disaster Information.
"But it's not come onshore and caused the disastrous damage that would happen if the eye of the cyclone had passed directly over," he told the French news agency AFP. Australia, France and New Zealand have formed a task force to get emergency supplies to any affected regions.
Australia's parliamentary secretary for foreign affairs and trade, Bruce Billson, said military planes and ships were already on standby.
"We can have action on the ground within hours of the countries affected requesting emergency assistance," Mr Billson told Radio Australia.
Once Cyclone Olaf has passed American Samoa it is forecast to move on towards the southern Cook Islands, which have just felt the effects of Cyclone Nancy.
The Cook Islands are also still recovering from significant damage caused by a Category Four cyclone, Meena, which struck nine days ago.