A catalytic converter-incorporated exhaust system is provided, which includes an exhaust tube through which exhaust gases emitted from an engine flow, and a muffler fluidly connected with a downstream end of the exhaust tube. This muffler includes a muffler casing having a plurality of expansion chambers defined therein, an exhaust introducing passage for introducing the exhaust gases from the exhaust tube into the expansion chambers in succession, two catalytic converters mounted in an downstream portion of the exhaust introducing passage and operable to substantially purify the exhaust gases, and an exhaust composition detecting sensor disposed outside the muffler casing in the exhaust introducing passage.