Fission track (FT) ages of the Omine Acidic Rocks, one of the Tertiary granitic rocks which occurs in the Outer Zone of the Median Tectonic Line, Southwest Japan, are determined in order to assess the timing of intrusion. Nine FT zircon (ZR) ages and one apatite (AP) age are obtained for igneous rocks, and four ZR ages for basement sandstone. Data for each pluton are concordant within a body representing the time of intrusion. The ZR ages from sandstone are concordant with the nearest pluton. The ages of plutons are classified into two groups statistically, suggesting that the Omine Acidic Rocks formed by two intrusive events. The Dorogawa, Tenguyama, Shiratani and Katago-Mukuro Dike are the older group with the weighted mean age of 16.8 ± 0.8 Ma, and the Kose pluton are the younger with an age of 14.2 ± 1.7 Ma. magma intrusion and tectonic framework at the time. Because of their possible complicated histories, the emplacement ages of granites should be estimated after investigation of their cooling histories by means of an age mapping and a combination of several dating techniques. At the beginning of studies on ages of the Outer Zone Granites, however, an age of each granite was estimated using data from one locality without investigation of its cooling history (Shibata and Nozawa, 1967).