For most kinds of surgeries an adequate anaesthesia is necessary. Three main components characterise an anaesthesia - the relaxation, the analgesia and the hypnosis. This paper treats the topic of the Propofol/Remifentanil induced hypnosis. We try to find a suitable model structure for the online identification of this process during a surgery. After a review of known models from literature an own model approach was developed and validated. By an offline optimisation study the parameter estimation problem of the defined cost function was examined. An online approach based on a recursive, iterative gradient algorithm was implemented. The quality of the identified parameters could be verified using measurements of surgeries.