Ship dynamics in ocean waves involve frequency-dependent added mass and radiation damping which can be estimated either by potential theory-based calculations or by experiments. With uniform forward speed, the added mass and damping matrices become asymmetric. In this paper, we attempt to use a system identification approach, specifically the reverse multiple input-single output (R-MISO) method, for coupled heave-pitch response (two degrees of freedom) of a ship moving with uniform forward speed in random ocean waves. The system mass matrix has both frequency-independent and frequency-dependent components, whereas its damping matrix has only frequency-dependent components. The frequency-dependent components of the mass and damping matrices are asymmetric. The excitation force and moment due to linear monochromatic waves which act on the system are assumed to be known and can be either calculated or obtained from experiments. For numerical illustration, a ship whose hydrodynamic behaviour has been computed by strip theory has been considered. The motion, as well as the loading, is simulated assuming Pierson-Moskowitz spectrum in conjunction with response amplitude operators from the strip theory code, and these results are analysed by the R-MISO method yielding frequency-dependent asymmetric coupled added mass and radiation damping coefficients satisfactorily. © 2010 Taylor & Francis.