An exhaust gas muffler is provided for an internal combustion engine, especially for an internal combustion engine in a manually-guided implement such as a power saw, a cut-off machine, or the like. The muffler has a housing having an inlet for exhaust gases and an outlet out of the housing. To achieve an after burning of exhaust gas in a straightforward manner, the exhaust gases in the housing flow through a reaction zone in which the exhaust gases circulate at least partially.