A linearized model is developed for the motions of a vessel steered by a windvane servomechanism. By neglect of several fast-time-scale effects, and assumption of linear hydrodynamics and mechanism, a second-order linear equation governing slow oscillations is derived, System dynamic stability is found to depend on certain vessel hydrodynamic coefficients, operating conditions, geometry, proportions and linkage ratios of the control system; this dependance is explored for several different vane and control combinations.