The cooling of a stream of hot product gas exiting from an outlet opening of a gasification reactor is made by way of two separate partial streams of cooling fluid such as a cooling gas, vapor or liquid. The first partial stream of the cooling fluid is fed from the outside substantially in a radial direction against an outer layer of the product gas stream. The second partial stream of cooling liquid is fed axially in a counter direction to the product gas stream to impinge against a central portion thereof. In this manner the path of mixing of the product gas with the cooling fluid is substantially shortened.