Varying-length cable systems are widely applied in a vast class of engineering problems which arise in industrial, civil, aerospatial, mechanical, and automotive applications. Due to external excitations, large oscillations can occur when cables are lifted up or down. This phenomenon is caused by resonance. In general, resonance is harmful, and can cause significient deformations and dynamic stresses in machinery and structures, and even can lead to accidents. Therefore, this doctoral dissertation is devoted to the study of transverse and longitudinal resonance phenomena and output feedback stabilization of varying-length cables....