Chinese balloons became a politically fraught topic in February when the United States shot down what it called a spy balloon, but that Beijing said was a civilian airship blown off course.
While China has in recent years ramped up military and political pressure on self-ruled democratic Taiwan, which it claims as its territory, the appearance of balloons is relatively rare.
The two sightings were made at 09:03 (0103 GMT) and 14:43 on Sunday, around 110 nautical miles (204 kilometres) northwest of the city of Keelung after crossing the strait, Taiwan's Defence Ministry said.
"The balloons headed east and disappeared at 09:36 and 16:35 respectively," it added in a statement.
A defence ministry spokesman said an initial analysis showed they were weather balloons.
The sighting comes after the ministry had said a balloon was spotted crossing the median line of the Taiwan Strait on December 8.
Defence Minister Chiu Kuo-cheng said at the time that it might be a sounding or a weather balloon that had drifted towards Taiwan on monsoon winds and that it could be used for meteorological research and data.
Taiwan is on high alert ahead of presidential elections next month, with Taipei and Washington warning Beijing not to exert any influence over the vote.
Beijing, which has vowed to one day seize Taiwan, has ramped up pressure since independence-leaning President Tsai Ing-wen came to power in 2016, regularly sending warplanes and vessels around the island.
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