Abstract: Method and apparatus to stabilize a columnar platform for deepwater offshore applications. An added mass stabilizer system is utilized to control first order heave, pitch, roll, surge and sway motions of the floating platform. The stabilizer is suspended beneath the platform by a set of tendons a sufficient distance to (1) enter a quiescent zone beneath the action of waves and currents, (2) provide a sufficiently long movement arm to resist pitch and roll torquing, and (3) incorporate sufficient flexibility into the suspension system to avoid shock loads. The stabilizer is sized to (a) provide sufficient submerged weight to maintain the tendons in constant tension and, (b) create adequate added mass (actual stabilizer weight plus mass of water moved by the stabilizer) to provide the desired control of first order motions. A secondary mooring system such as a spring-buoy mooring or dynamic positioning system can be provided to control drift produced by higher order motions and first order yaw.