Broaching, surf-riding, and capsizing of ships and offshore structures are transient wave-structure interactions which imply high risks for crew, vessel and cargo. As nonlinear effects are of great importance, time-domain investigations are indispensable. For unveiling the associated driving mechanism of these critical motions, it is desirable to analyze the cause-reaction chains in detail: Depending on the transient wave elevation, we obtain an instationary pressure distribution on the wetted surface of the cruising vessel. Resulting forces and moments excite vessel motions in six degrees of freedom. Based on the linear panel-method program for transient wave-body interactions, TiMIT [Korsmeyer et al. (1999)], this paper investigates seakeeping characteristics of offshore structures with forward speed. Results are presented in frequency and time domain. The procedure allows to identify critical seaways, and to analyze cause-reaction chains in deterministic wave sequences where critical and steep wave packets are embedded in random seas. The detailed evaluation reveals that large roll and pitch motions are easily reduced by variation of course and speed. For investigating the mechanism of wave/structure interactions, this paper introduces the relevant time-domain methodology, and indicates how nonlinear wave characteristics can be introduced in the time-stepping analysis. In subsequent steps nonlinear wave/structure interactions will also be considered.