In the paper, a two-degrees-of-freedom ship model with quadratic coupled pitch and roll modes under sinusoidal harmonic excitation is considered. A straightforward expansion allows for obtaining both the resonant values of external excitation frequency and one internal resonance. The Multiple Scales method yields the first-order expansions for the special resonant case where the excitation frequency is close to the roll frequency. The time series and the frequency – amplitude curves provided by numerical integration are contrasted with those given by the perturbation technique for different combination of system’s parameters. If the parameters are selected within the pre-ordered range, the results of both methods are in excellent or, at least, in pretty good agreement.