A connection adapter 7, which is disposed between the appliance-side exhaust section 5 of each combustion device 2 of a combined combustion device 1 and a collective exhaust cylinder 10, comprises: a first exhaust pipe 70, the lower end of which is connected to an appliance-side exhaust pipe 50; a backflow prevention valve 75 that is provided at the upper-end opening of the first exhaust pipe 70 and prevents backflow of combustion exhaust from the collective exhaust cylinder 10 to an appliance body 20 while combustion is stopped; and a second exhaust pipe 80 that is provided so as to surround the outer periphery of the first exhaust pipe 70, and connected at the lower end to a drain water recovery unit 55 and at the upper end to the collective exhaust cylinder 10.