Linear and 2nd order theories, which are being widely applied in marine hydrodynamics, are not always mathematically consistent or applicable in practice. In this talk, we discuss the challenges in the conventional seakeeping models concerning large horizontal motions and higher derivatives in body boundary conditions, followed by an introduction of a more consistent formulation in the body-fixed coordinate system. As important elements of the numerical implementation, a new class of explicit timeintegration schemes for convection equations, together with a new set of optimized weighted least-squares (WLS) filters, will be presented. Practical examples of the KVLCC2 ship and a spar floating offshore wind turbine (FOWT) will be given to demonstrate the advantage of using a consistent formulation。