The asbestos tape was originally used to help hold the ducting together at the joints, and to assist in preventing air from escaping from the system at those joints. Modern duct tape is asbestos-free.

We aren't talking about a lot of asbestos here. You can remove the old tape yourself. Moisten the old tape and remove as much as possible. Then, simply retape all the joints with two or three winds of new 2-inch-wide silver duct tape. As a contractor we are allowed to work on up to about a 120' of asbestos piping without special restrictions. A few inches of asbestos tape falls well within safe limits for us - and you.

Since winter is just around the corner, we thought a suggestion might be in order here. Since you can see the duct tape on your metal heat-supply ducts, it is apparent to us that they are not insulated. While you are at the store getting duct tape, purchase a few rolls of 1-inch-thick by 12-inch-wide insulation and wrap those ducts. Save yourself some heating-bill bucks this winter.