Of the physiological subsystems involved in glucose metabolism, all have now been modelled with continuous-time compartmental models except the gut. To address this omission, three progressively more complex models of the conversion of food by the gut into the rate of appearance of glucose in plasma were identified, using two different sample input foods which were tested on a type 1 diabetic patient. The minimal model that achieved a reasonable match with measured values had one compartment. Two model parameters specific to the food modelled were glycaemic value (grams of glucose per gram of food), and the fractional turnover rate, corresponding to a combination of the gastric emptying time constant and other rate limiting metabolic processes. Parameters specific to the individual were compartmental volumes, specifically for the glucose distribution space. It was only possible to achieve an adequate model prediction with a one compartmental model by explicitly incorporating transport delay into the model. By combining this model with models of insulin production and glucose disposal, the glycaemic response of an identified food may also be predicted for patients with type 2 diabetes mellitus. This predicted responses, along with the predicted response for bread or glucose, enables calculation of the Glycaemic Index for the food from its glycaemic value, time constant, and transport delay, along with the insulin production and glucose disposal model parameters for the individual patient. These three minimal model parameters therefore embody all the information of the Glycaemic Index, and more, allowing a continuous prediction of the effect of eating a given food over time. Together with a means of combining the parameters of individual foods into a combination set for a composite meal, this minimal model could enable diabetic patients to predict the time course of glycaemic action for a meal and to adjust treatment accordingly.