Abstract: A mowing machine has a machine frame, front and rear wheels rotatably mounted on the machine frame, a control handle mounted on the machine frame, and a cutting assembly suspended by the machine frame for angular movement about a swing axis extending along a direction in which the mowing machine can travel straight. The front and rear wheels comprise single wheels, respectively, so that the mowing machine is two-wheeled. The machine frame, the front and rear wheels, and the control handle jointly serve as a non-swingable section, and the cutting assembly serves as a swingable section, the swingable section being suspended in offset relationship to the swing axis, the swingable section including a guide member for keeping the cutting assembly spaced from ground. The mowing machine may further include an angular range limiting mechanism for limiting the range of angular movement of the swingable section.