Cyclone Donna has weakened to a tropical low, with its centre moving away from New Caledonia.
The storm caused damage on Lifou, ripping off roofs and uprooting trees, but while it was a category three storm its centre passed further east of the Loyalty Islands than forecast.
Power is being restored after Lifou's network was turned off for the worst of the storm.
The phone network has also been disturbed, with landlines down because of power cuts.
Late this morning, 18 mobile phone transmitters were still out of action in areas close to the cyclone's path.
Domestic flights have resumed, with 20 scheduled flights planned for the rest of Wednesday.