A method for the diagnosis of an air supply circuit supplying air to a burner of an exhaust gas after-treatment system for an exhaust system of an internal combustion engine, wherein the air supply circuit is provided with a pumping device housed along a first duct adjusted by a shut-off valve. The method entails housing a first pressure sensor along the first duct interposed between the pumping device and the burner; housing a second pressure sensor along a second duct out of the burner; acquiring the pressure signals detected by said first and second pressure sensors; and diagnosing faults and/or malfunctions in the air supply circuit depending on the pressure signals detected by said first and second pressure sensors.