The growing use of antennas for data transmission calls for the installation of growing number of high towers, with the cable-stayed towers standing out. These structures are composed of a central mast and several levels of stays. These towers are slender structures and exhibit a highly non-linear behavior under static and dynamic loads, due to the mast-cable interaction and the tower height. The objective of this work is to study the influence of the nonlinearity on the static and dynamic behavior of a cable-stayed tower. For this, finite element models of cable-stayed towers with two levels of pre-tensioned cables are developed. Two cable disposition geometries are considered: fan and parallel. In particular, the effect of the rupture of one or more cables and the elastoplastic behavior of the cable-stayed tower materials on the stability and non-linear vibrations of the structure is investigated. Initially, the linear behavior of the structure is evaluated through the natural frequencies and critical loads. Next, the non-linear equilibrium paths of each model are obtained, applying the concept of modal imperfection. Finally, free and forced damped vibration analysis is performed. For this purpose, responses in time and phase plane, Fourier transforms and spectrographs are used. In all cases, the effect of the loss of cables and the plastification of the elements on the load capacity, stability and displacements of the structure is analyzed in detail. The results demonstrate that the loss of cables and plastification of elements have a great influence on natural frequencies and critical loads. Under such conditions, non-linear behavior with loss of load capacity and significant increase in displacements, velocities and accelerations stand out, and highlight the need for investigation of the nonlinear behavior of this type of structure.