Dynamic response analysis of offshore triceratops with stiffened buoyant legs under impact and non-impact waves is presented. Triceratops is relatively new-generation complaint platform being explored in the recent past for its suitability in ultra-deep waters. Buoyant legs support the deck through ball joints, which partially isolate the deck by not transferring rotation from legs to the deck. Buoyant legs are interconnected using equally spaced stiffeners, inducing more integral action in dispersing the encountered wave loads. Two typical nonlinear waves under very high sea state are used to simulate impact and non-impact waves. Parameters of JONSWAP spectrum are chosen to produce waves with high vertical and horizontal asymmetries. Impact waves are simulated by steep, front asymmetric waves while non-impact waves are simulated using Stokes nonlinear irregular waves. Based on the numerical analyses presented, it is seen that the platform experiences both steady state (springing) and transient response (ringing) of high amplitudes. Response of the deck shows significant reduction in rotational degrees-of-freedom due to isolation offered by ball joints. Weak-asymmetric waves, resulting in non-impact waves cause steady state response. Beat phenomenon is noticed in almost all degrees-of-freedom but values in sway, roll and yaw are considerably low as angle of incidence is zero degrees. Impact waves cause response in higher frequencies; bursting nature of pitch response is a clear manifestation of the effect of impact waves on buoyant legs. Non-impact waves cause response similar to that of a beating phenomenon in all active degrees-of-freedom, which otherwise would not be present under normal loading. Power spectral density plots show energy content of response for a wide bandwidth of frequencies, indicating an alarming behaviour apart from being highly nonlinear. Heave, being one of the stiff degrees-of-freedom is triggered under non-impact waves, which resulted in tether tension variation under non-impact waves as well. Reduced deck response aids functional requirements of triceratops even under impact and non-impact waves. Stiffened group of buoyant legs enable a monolithic behaviour, enhancing stiffness in vertical plane. © 2017 Techno-Press, Ltd.