NOVELTY - Non-gaseous hydrocarbonaceous material is pyrolyzed in a pyrolysis chamber, and produced primary fuel gas mixture and pyrolysis liquid are introduced into a chamber (II) and heated at preset conditions, to produce additional fuel gases and additional solid carbonaceous residue without altering the composition of primary fuel gas mixture. The primary fuel gas mixture and additional fuel gas are removed, and air, oxygen, carbon dioxide or steam is introduced into the chambers, and at least partial removal of carbonaceous residue is carried out. Thus, fuel gases are produced.    USE - For producing fuel gases from non-gaseous hydrocarbonaceous material(s), particularly mixed solid waste material, using two-stage reaction apparatus.    ADVANTAGE - The catalyst in chamber (II) is regenerated effectively. Light gases such as methane, hydrogen, carbon monoxide, carbon dioxide and reactor carbon rich char are produced by pyrolysis processing of solid waste resource. Significant amounts of liquid products are formed under less severe pyrolysis conditions and are cracked completely to gases as temperature is raised.    DETAILED DESCRIPTION - Non-gaseous hydrocarbonaceous material is introduced into a pyrolysis chamber (I) (12) comprising stage (I) of a two-stage apparatus (10). The material is pyrolyzed in the chamber to produce a primary fuel gas mixture, a pyrolysis liquid and carbonaceous residue (I). The primary fuel gas mixture and pyrolysis liquid are introduced into a chamber (II) (14) comprising stage (II) of the apparatus and having a catalyst. The liquid is heated in a non-oxidizing atmosphere at 900-1100degreesC which is higher than the temperature by which pyrolysis is carried out. Additional fuel gases and additional solid carbonaceous residue are produced without altering the composition of primary fuel gas mixture. The primary fuel gas mixture and additional fuel gas are removed from the chamber (II), and air, oxygen, carbon dioxide or steam is introduced into each of the chambers, and at least partial removal of carbonaceous residue is carried out. Thus, fuel gases are produced.    DESCRIPTION OF DRAWING(S) - The figure shows a power generation apparatus.    Reactor (I) (10)    Chamber (I) (12)    Chamber (II) (14)    Flow control unit (18)    Power generator (20)