At 1130 a.m.(0330 GMT), the Central Weather Bureau said the storm was 210 kilometers (132 miles) east of Taiwan's northern tip, packing sustained winds of 108 kmh (68 mph) with gusts of up to 137 kmh. It was expected to pass just north of the capital of Taipei sometime after nightfall.
An increase of 10 kph in sustained wind speed would cause the storm to be upgraded to typhoon status.
Earlier this week, Trami wreaked havoc in the Philippines, causing eight deaths and flooding wide swathes of Manila.
In Taiwan, forecasters expect up to 300 mm (12 inches) of rain to fall in Taipei, and perhaps twice that amount in heavily mountainous areas farther to the south, where landslides pose a major threat to remote communities.
One landslide has already been reported north of Taipei.
Late Tuesday government officials ordered schools and offices in Taipei and in some surrounding regions to close because of safety concerns.
They also evacuated more than 1,000 residents from an outlying island they believe to be threatened by the oncoming storm.
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