The hyperglycemia that occurs during diabetes mellitus is accompanied by

ketoacidosis

Explanation:

Severe cases of hyperglycemia can lead a condition called ketoacidosis. It develops when your body doesn't have enough insulin (case of diabetes mellitus). Without insulin, your body can't use glucose for fuel, so your body starting breaks down fats to use as energy.  The waste products from breaking fats is called ketones. Your body cannot tolerate large amounts of ketones and will try to get rid of them through the urine. Unfortunately, the body cannot release all the ketones and they build up in your blood, which can lead to ketoacidosis.