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A new method for the accurate discrete technique of directional spectra is proposed for the simulation of the second-order incident potential of directional seas, and a second-order time-domain analysis program is developed for nonlinear wave forces on marine structures in multidirectional irregular seas. The boundary-value problems for the diffracted potential are solved by a higher-order boundary element method (HOBEM). The fourth-order Adams–Bashforth–Moulton method combined with the Newton–Raphson iteration is implemented for time integration. The present method is validated by comparison with the published frequency-domain results for a bottom-mounted vertical cylinder in bichromatic bidirectional waves. The second-order diffracted forces on a truncated cylinder are examined for different combinations of storms and swell seas, and major efforts are focused on investigating the effects of wave directionality, directional spreading, and the spectral peak frequency of mixed seas.