In a method of making an exhaust gas collector, a collector housing is made from a tubular blank, and subsequently, an inlet duct is formed through a widening process to provide a substantially rectangular cross section with rounded narrow sides. The inlet duct is provided with a head flange. At the outlet side, the collector housing is necked by a press-forming process so as to shape an outlet duct having a substantially circular cross section which is reduced in size compared to the cross section of the collector housing. Attached to the outlet duct is an end flange.