The invention relates to a health surveillance system comprising a medical diagnosis which is made by a medically-qualified person (11) in relation to a patient who is being monitored remotely, e.g. at home, via a communication network. The invention is characterised in that the medically-qualified person (11) links medical data (2) to health actions (3) in a server (1) using surveillance rules. The invention is further characterised in that the server (1) programs a remote terminal (9) which is located close to the patient, such that the remote terminal (9) uses an automatism (5) which applies the surveillance rules to the medical data supplied to the terminal by at least one sensor (8) which is associated with the patient and/or by a man/machine interface of the remote terminal (13) and/or by a man/machine interface of a network station (12) and/or by the network (7).