This is completely dependent on the day that you decide to elect to enroll in COBRA insurance.  If you decide  to enroll in COBRA insurance right away, you will just be responsible f or the first premium.  However, if you wanted until the last day to enroll, you would have to pay 2 months of premiums.  This is because COBRA insurance is retroactive back to the date your insurance coverage would have stopped and you need to pay to cover that full period.  You can find out exactly what you need to pay by contacting your group health insurance plan.