In this paper, the rolling motion of a ship in a random beam sea is considered. The uncoupled roll motion equation is decribed by a second order differential equation nonlinear both in restoring and damping. By means of a perturbative method, an approximate solution has been obtained in the form of a modified RAO including the main nonlinear coefficients. In this way their relative importance can be discussed. Moreover the calculation is straightforward, so allowing an extension of the conventional linear seakeeping calculations. The analytical results compare well with numerical simulations made by using the spectrum of a moderate sea.
