The dynamic stability of a typical offshore service vessel operating under stability critical operating conditions was investigated. Excessive roll motions and relative motions at the stern were studied for two loading conditions for ship speeds ranging from zero to the design speed. A linear frequency-domain seakeeping analysis was followed by nonlinear time-domain simulations of ship motions in waves. Based on results from these methods, critical scenarios were selected and simulated using finite-volume solvers of the Reynolds-averaged Navier-Stokes equations to understand the phenomena related to dynamically unstable ship motions and to confirm the results of the simpler analysis methods. The results revealed the possibility of excessive roll motions and water run-up on deck; countermeasures such as a ship-specific operational guidance are discussed.