Stability of the response of an articulated loading platform under regular wave, modeled as a SDOF nonlinear oscillator, is investigated. Relative velocity square drag force for harmonic wave appearing in the right hand side of the equation of motion is mathematically treated to bring the velocity dependent nonlinear hydrodynamic damping term to the left hand side of the equation of motion. Use of these two techniques makes the equation of motion amenable to the application of method IHBC. In order to trace different branches of the response curve and investigate different instability phenomena that may exist, the commonly used incremental harmonic balance method (IHB) is modified and integrated with an arc-length continuation technique to develop into incremental harmonic balance continuation (IHBC) method. Further, a technique for treating the nonlinear hydrodynamic damping term using a concept of distribution theory has been developed. The stability of the solution is investigated by the Floquet theory using Hsu’s scheme. The stable solutions obtained by the IHBC method are compared with those obtained by the numerical integration of equation of motion wherever applicable.