Q: I turned 65 and signed up for Medicare A. At that time I was employed and under my employer group plan. In April I was termed and they offered to pay for my Cobra for 6 months. Can I be coverend under Cobra? A: Once you are eligible for Medicare, COBRA will no longer be available to you. However, COBRA will be available for your dependants and they have the right to elect COBRA for 36 months.