To meet stringent emission standards and improve performance of two-stroke crankcase-scavenged engines, the muffler (13) of the engine is provided with mixing means (130, 31) for mixing the exhaust gases (42) resulting from the mixture participating in combustion and gases resulting from scavenging, so that a substantially homogenous gaseous mixture is formed within the muffler (13), and means (81) for sensing oxygen concentration is located in the homogeneous gaseous mixture and are configured to provide an output value to a control unit (80) for controlling supply of fuel to the engine and thereby the air-fuel ratio in the combustion chamber (41). The muffler (13) suitably is provided with a catalytic element (140), preferably a three-way catalyst. The engine (1) preferably is a stratified charge engine.