Transonic flutter characteristics of a NAGA64A010 airfoil with two-degrees-of-freedom are investigated theoretically. For this purpose, an unsteady aerodynamic code based on the transonic small perturbation equation, which can be applied for the wide range of the reduced frequency based on semi-chord(0 less than or equal to k less than or equal to 0.5) and Mach number(from subcritical to above Mach 1), has been developed. The finite differnce scheme employed in the code is a time-marching, semi-implicit and implicit two-sweep procedure. Flutter calculations are performed for two typical binary systems, one of which simulates the vibrational characteristics of a typical streamwise section of a sweptback wing, and the other of which simulates that of an unswept wing. A sharp transonic dip of the flutter boundary has been predicted for the former case while the relatively mild dip for the latter. For the purpose of identifying the possible mechanism of the transonic dip phenomenon, examinations are made of not only the flutter modes and frequencies but also the shock wave patterns and the unsteady load distributions at each Mach numbers corresponding to the flutter boundary. As a result of these examinations, it is concluded that the mechanism of the single-degree-of-freedom flutter, which is casued by the large negative damping produced by the phase lag of the shock wave motion, is dominating the flutters at the bottom of the transonic dip when the mass ratio is relatively large.