There were no immediate reports of damage or casualties.
The first quake struck at 09:59 am (0159 GMT) with an epicenter 15 kilometers (9.3 miles) south of the eastern coastal town of Ilan. It originated eight kilometers underground.
The second tremor hit at 12:56 pm (0456 GMT) with an epicenter 11 kilometers north of Ilan. It's origin was 75 kilometers underground.
Taiwan's worst recorded earthquake, measuring 7.6 on the Richter scale, struck in September 1999, leaving some 2,400 people dead.