A dynamical network model of insulin-glucose interactions in subjects with Type I Diabetes was developed and applied to data sets for 40 subjects. Each data set contained the amount of dextrose + insulin infused and blood glucose (BG) determinations, sampled every 5 minutes during a one-hour standardized euglycemic hyperinsulinemic clamp and a subsequent one-hour BG reduction to moderate hypoglycemic levels. The model approximated the temporal pattern of BG and on that basis predicted the counterregulatory response of each subject. The nonlinear fits explained more than 95% of the variance of subjects' BG fluctuations, with a median coefficient of determination 97.7%. For all subjects the model-predicted counterregulatory responses correlated with measured plasma epinephrine concentrations. The observed nadirs of BG during the tests correlated negatively with the model-predicted insulin utilization coefficient (r = -0.51, p < 0.001) and counterregulation rates (r = -0.63, p < 0.001). Subjects with a history of multiple severe hypoglycemic episodes demonstrated slower onset of counterregulation compared to subjects with no such history (p < 0.03).