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Type-One Diabetes Mellitus (T1DM) is a chronic disease characterized by the elevation of glucose levels within patient's blood. It can lead to serious complications including kidney and heart diseases, stroke, and blindness. The proper treatment of diabetes, on the other hand, can lead to a normal longevity. Yet such a treatment requires tight glycemic control which increases the risk of developing hypoglycemia; a sudden drop in patients' blood glucose levels that could lead to coma and possibly death. Continuous Glucose Monitoring (CGM) devices placed on a patient body, measure glucose levels every few minutes. These devices can also detect hypoglycemia. Yet detecting hypoglycemia sometimes is too late for a patient to take proper action, so a better approach is to predict the hypoglycemic events ahead of time and alarm the patient to such occurrences. In this research, the authors develop a system that involves a special type of Artificial Neural Networks (ANN), the Time-Sensitive ANN (TS-ANN), to predict hypoglycemia events ahead of time and within a prediction horizon of thirty minutes. This period should be long enough to enable diabetic patients to avoid hypoglycemia by taking a proper action. A TS-ANN based system that is able to predict hypoglycemia events have been developed and tested with high accuracy results (average specificity of 98.2%, average accuracy of 97.6% and average sensitivity of 80.19% with a maximum value reaching 93%).