The paper discusses the stability problem of a synchronous generator connected to an infinite bus. Owing to the time-consuming tuning of a conventional power-system stabiliser and its non-optimal damping in the entire operating range, simple adaptive control is proposed. The following are presented: the influence of the operating point (loading) on the eigenvalues of a simplified linearised model of a synchronous generator; the model reference adaptive control for almost strictly positive real plants and the simple adaptive power-system stabiliser derived from the presented model reference adaptive control theory. The control-system design was carried out for the simplified linearised model of a synchronous generator, but for the evaluation of the control-system performance in the single machine case under small-signal and large-signal disturbances, the full-order non-linear model of the synchronous generator was used. Simulation and experimental results show the applicability of the presented approach.