For offshore floating structures, such as semi-submersible platforms, TLPs and SPARs viscous drag forces on columns and truss work may give significant contributions to the low frequency loads and responses. Calculating such loads based on just potential theory, which is common, can be significantly insufficient. The viscous loads depend nonlinearly on waves and current in combination. In particular, correct low frequency loading is important in the design of mooring systems for offshore structures. The paper describes some intermediate results from a project aiming at formulating dynamic frequency domain models for low frequency viscous excitation and damping of floating structures subjected to current and irregular waves. The basis for the models is the drag term in the Morison equation. Different models are formulated for the submerged parts of the structure and the splash zones. At present basic models are formulated for a narrow submerged strip of a vertical cylinder and the splash zone of the same. The loads are quantified in terms of power spectral density functions. To be able to formulate expressions for the power spectra the Morison drag force model is approximated by simple polynomials in the water speed. For the submerged strip an alternative method exists, that uses a series expansion for the force spectrum.