Conventional linear added mass and damping can be obtained when a floating body is forced to oscillate in the calm water. However, with the presence of the incident waves, there exists an alternative source of added mass and damping caused by the nonlinear interactions between waves and low-frequency oscillations. Proportional to the square of the wave amplitude, they are called the wave drift added mass and the wave drift damping. The problem of a circular cylinder array slowly oscillating in both diffraction and radiation wave fields is considered in the present work. The frequency of the low-frequency oscillation is assumed to be much smaller than the wave frequency. Perturbation expansion based on two time scales is performed to simplify the problem. Wave loads including the wave drift added mass are formulated by integration of the hydrodynamic pressure over the instantaneous wetted body surface.