Time-domain models were developed to predict the response of a tethered buoy subject to hydrodynamic loadings. A coupled analysis of the interaction of a buoy and its mooring is included and three-dimensional response is assumed. External loadings include hydrodynamic forces, tethers tensions, wind loadings and the weight of both cable and buoy. System nonlinearities include, large rotational and translational motions, and non-conservative fluid loadings. The mooring problem is formulated as a nonlinear two-point-boundary-value-problem. The problem is then converted to a combine initial-value and boundary-value problem to a discrete boundary-value problem at particular time, using a Newmark-like difference formula. At each instant in time the nonlinear boundary-value problem is solved by direct integration and using a successive iterative algorithm, such that boundary conditions are always satisfied. Buoy equations of motion are derived by both a small angle assumption and a large angle assumption. The small angle formulation uses the Eulerian angle for rotational coordinates. Coupling between the buoy and cable is performed by adopting the buoy equations of motion as boundary conditions at one end for the mooring problem. The rotational coordinates for the large angle formulation are represented by Euler parameters. The large angle formulation is solved by a predictor-corrector type of time integration of buoy motions constrained by tether forces. Coupling between the buoy and moorings is then enforced through matching of the velocity of the tether attachment points on the buoy with velocity of the tether ends; the velocities of tether attachment points serve as boundary conditions for the various mooring cables attached. Multiple time steps are used to account for different sizes of integration time step required for stability of solution in the buoy and tether. Numerical examples are provided to contrast the validity and capability of the formulations and solution techniques. Responses of three types of buoy (sphere, spar and disc) are predicted by the present models and compared to results obtained by experiments. Application of the present model to solve a multi-leg/multi-point mooring system is also provided. / Graduation date: 1996