The ferry crossing from Larne to Cairnryan has been suspended, while roads have been closed across the region, with police urging motorists to be cautious on other routes.
Fallen trees have caused damage to properties and have blocked roads.
Northern Ireland Electricity (NIE) also said fallen branches and trees had already damaged power lines, disrupting electricity supplies in some areas.
It said hundreds of extra engineers had been called in to cope with any major problems.
Spokesman Sara McClintock said: "Customers should take precautionary measures in the event of a power cut."
Meanwhile, the storms have forced a further delay in plans to deal with a damaged oil tanker in Belfast Lough.
After the vessel suffered a crack in its upperdeck, its 54,000 tonnes of oil was to be transferred to a separate carrier.
The task should have started on Monday, but has now been delayed because of the weather.
A spokesman said there was currently no risk to the environment and officials wanted to wait until conditions were calmer.
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