Generally, COBRA benefits are not provided if a person has other insurance. The insurance company then reprocesses the claims reversing the payouts. It usually takes about a month for all the providers to reverse payment receipts. You need to make sure you comply with the other insurance companies rules for notification, so they process the claims as primary. You should followup with each bill incurred during the period to make sure the provider re-bills the other insurance and it is paid. Make sure to document the original process dates on the inital claim submission to the former insurance in case a timeliness issue comes up. The insurance company will honor the original submission date to the other company if you can prove it.