To provide a connection structure which is small in number of parts and is easy of connection and is strong, in one which connects a heat exchanger for cooling of cooling water of an engine mainly for an automobile with a heat exchanger for a car air conditioner in a body.

The end of the header pipe 2 of the first heat exchanger 3 is plastically transformed flat to be blocked, and also the end is bent in L shape in cross section to form an attachment 7. Then, the attachment 7 is provided with a connection hole 8, and the first heat exchanger 3 is fastened and fixed to the tank 5 of the second heat exchanger 6 or the strong member 10 around the second core 4 through a fastening bolt 9 inserted into the connection hole 8.