In this paper, we prove that the simultaneous Pell equations x 2 − (m 2 − 1)y 2 = 1, z 2 − (n 2 − 1)y 2 = 1 have only positive integer solution (x, y, z) = (m, 1, n) if m < n ≤ m + m ε , 0 < ε < 1 and m ≥ 202304 1 1−ε . Using a computational reduction method we can omit the lower bound for m when m < n ≤ m 1 5 . Moreover, we apply our main result to a family of Thue equations in two parameters studied by Jadrijević [?]- [?].