The present invention provides a technique which enables exhaust gas recirculation to be implemented satisfactorily in a single cylinder air-cooled engine in which thinning of a cylinder head wall portion has been carried out in order to ensure cooling performance. In this single cylinder air-cooled engine, an exhaust gas recirculation EGR pipe which recirculates exhaust gas from an exhaust side to an intake side is provided outside a cylinder head, and the EGR pipe is disposed between a bonnet covering an upper portion of the cylinder head and an exhaust muffler provided on a side portion ofthe cylinder head. The EGR pipe is divided into an intake side pipe connected to the intake side and an exhaust side pipe connected to the exhaust side, and is configured by connecting the intake sidepipe and the exhaust side pipe together by means of a detachable connecting member.