A muffler assembly for an internal combustion engine of a portable handheld work apparatus such as a motor-driven chain saw, cutoff machine or the like includes an exhaust-gas muffler (1) which has a muffler housing (10). The muffler housing (10) is formed essentially from two half shells (24, 25) connected substantially fluid-tight to each other. The interior space of the muffler housing (10) includes at least two chambers (2, 3) which are partitioned from each other by a partition wall (4). A catalytic converter (5) is mounted in the partition wall (4). In the interior space of the muffler housing (10), an exhaust-gas inlet (6) opens which is connected to an exhaust-gas stub (9) of the cylinder (8) of the engine. The exhaust-gas muffler has an exhaust-gas outlet (7) which conducts exhaust gas from the interior space. The exhaust-gas muffler (1) is connected with threaded fasteners at at least three attachment points (22, 23) to the cylinder (8) in order to obtain a good fixation of the exhaust-gas muffler on the cylinder (8) of the engine. At least two attachment points (22) are arranged in the region of the exhaust-gas stub (9).