Alessia has been downgraded to below cyclone strength, but strong winds and heavy rain are still lashing the Top End.
Ex-Tropical Cyclone Alessia was about 110km south of Darwin overnight, with winds near the centre below gale force, but still packing a punch at about 95km/h.
The storm weakened after making landfall 6.30pm (CST) on Sunday.
The Bureau of Meteorology downgraded the cyclone warnings for areas from Darwin to the WA border, but says heavy rain is still likely to cause localised flooding and may lead to significant stream rises in the Darwin-Daly, Arnhem and western Roper-McArthur Districts.
The storm is tracking towards the east at about 30km/h.
Authorities had been warning residents to prepare for the Category one tropical cyclone's arrival on Sunday.
Forecaster Todd Smith told reporters in Darwin that there may be downed trees and power lines to contend with on Monday, but that they weren't expecting winds to be too destructive.
It will be business as usual on Monday morning, with schools open and the public service running, Chief Minister Adam Giles says.
The airport and port are also still operating.
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