Tonic inhibition has been found experimentally in single neurons and a ects the activity of neural populations. This kind of inhibition is supposed to set the background or resting level of neural activity and plays a role in the brains arousal system, e.g. during general anaesthesia. The work shows how to involve tonic inhibition in population rate-coding models by deriving a novel transfer function. The analytical and numerical study of the novel transfer function reveals the impact of tonic inhibition on the population ring rate. Finally, a rst application to a recent neural eld model for general anaesthesia discusses the origin of the loss of consciousness during anaesthesia