This chapter provides a brief introduction to the linear wave theory that forms the basis for the derivation of the wave forces on the structure. It discusses general derivation of the structural equations of motion. Analytical representations of the fluid-structure interaction are complicated by many phenomena, such as turbulent flow about the structure, and the nonlinear relation between water particle kinematics and water surface displacement. The nonlinear equations of motion for a compliant offshore structure such as an articulated tower, a tension leg platform and a riser are derived. It is assumed that the deck motion and the cable/column attached to it are coupled, thus two equations are derived. Nonlinearities due to geometry and external forces are included in the analysis. The equation of motion for the lateral displacement is a nonlinear partial differential equation with time-dependent coefficients.