This thesis deals with the stability of bicycles in the upright motion with main focus on the wobble mode. Wobble, which is related to the more general class of wheel-shimmy, is a self-exited oscillation of a bicycle's steering wheel about the steering axis and is perceived unpleasant or unnerving, or may also be hazardous if not controlled by the rider in time. The influences on the wobble mode of a specific trekking bike for women, with shows a pronounced unstable wobble mode at certain speeds, is investigated both on the basis of a mathematical model and on test runs. For numerical analysis a mathematical model of the trekking bicycle is required which takes the frame flexibility, the side slip of the tires and also the dynamic properties of tyre force generation into account. The linearized equations of motion with respect to the upright rectilinear motion are derived from the nonlinear equations and are given in the thesis. To compare numerical findings with observations form test runs the trekking bicycle has been equipped with measurement devices, which records the steering angle, speed and 3-axis accelerations and angular velocities. To validate the mathematical model, the eigenvalues of the measured wobble motion are compared with those of the numeric analysis. From the numerical analysis parameters with a significant influence on the wobble mode could be identified.