Study of dynamic stability phenomenon in transient systems has always created interest amongst the researchers because of its inherent non-linearities. Offshore structures subjected to wave, earthquake or wind loads or a combination of these loads show non-linear transient behaviour. As oceanic waves are better modelled as stochastic process, there is a need to investigate the stochastic stability of flexible offshore structures as well. Present study has been carried out to determine seismic response of Single Hinged Articulated Tower (SHAT) under different categories of wave loads and earthquake followed by its dynamic stability analysis. Different phases of wave/earthquake loading on SHAT have been explored to investigate dynamic instabilities existing during each phase. Two dimensional phase plots have been used to identify phases of dynamic instability existing within the responses of SHAT under various conditions of loading.