Diabetes is a group of metabolic diseases characterized by hyperglycaemia resulting from defects in insulin secretion, insulin action, or both. Several models have been developed for describing the glucose-insulin system. Silber and Jauslin developed a semi-mechanistic integrated glucose insulin (IGI) model which simultaneously describe glucose and insulin profiles in either healthy subjects or type 2 diabetis mellitus (T2DM) patients. The model was developed for describing the basal system, i.e. when no drugs are present in the body. In this thesis the IGI model was extended to also include the effects of anti-diabetic drugs on glucose homeostasis. The model was extended to describe postprandial glucose and insulin excursions in T2DM patients treated with either biphasic insulin aspart or the GLP-1 receptor agonist liraglutide. These extensions make the model a useful tool in drug development as it can be used for elucidating the effects of new products as well as for clinical trial simulation. In this thesis several modelling tasks were also performed to get a more mechanistic description of the glucose-insulin system. A model was developed which describes the release of the incretin hormones glucosedependent insulinotropic polypeptide and glucagon-like peptide-1 following the ingestion of various glucose doses. The effects of these hormones on the beta cell function were incorporated in a model describing both the C-peptide and insulin concentrations in healthy subjects and T2DM patients during either an oral glucose tolerance test or an isoglycaemic intravenous glucose infusion. By including measurements of both C-peptide and insulin concentrations in the model it could also be used to characterize the hepatic extraction of insulin.