This contribution focuses on the dynamical modeling and control of a selfbalancing bicycle. The bicycle is equipped with two flywheels rotating at constant speed mounted via a hinge that is actuated by an additional motor and allows for rotation about the vertical axis. Due to the balance of angular momentum, a torque is generated around the axis perpendicular to the hinge and spinning axis, i.e. an axis along the forward motion direction. This gyroscopic effect is exploited for the stabilization of the bicycle. Two cases are distinguished: 1) For the stabilization of the nonmoving bicycle an LQcontroller based on a linear model is used. 2) For the moving bicycle, a nonlinear dynamic model in terms of nonholonomic velocities is derived and based on the linearized model at constant driving speeds the stability of the bicycle is analyzed. The model reveals the selfstabilization behavior of a bicycle without flywheels. At a speed of about 17km/h, the linearized model has only eigenvalues with negative real parts and is hence stable. Experimental as well as simulation results are presented.