In the present work the performance of a pendulum absorber in the vibration control of tall and slender towers, caused by dynamic loads, such as, environmental loads, is studied in detail. Due to the possibility of large amplitude oscillations, the non-linearity of the pendulum is considered in the modeling of the problem. The main objective of this research is to study the behavior of the tower-pendulum system, submitted to a harmonic load, in the nonlinear regimen, with emphasis on general aspects related to its dynamic stability. It is presented, initially, the formulation necessary for the derivation of the system´s energy functional, both for the linear and the nonlinear cases, from which the partial differential equations of motion are derived and the vibration frequencies and related vibration modes are obtained. Then, based on the modal analysis of the column-pendulum system, a two degrees of freedom model, capable of describing with precision the behavior of the system in the neighborhood of the fundamental frequency of the column is derived, from which the equations of motion and the nonlinear state-space equations are obtained. A detailed parametric analysis of the nonlinear oscillations of the system is carried out. It shows that the pendulum may reduce or amplify the response of the column. The results show a marked influence of the geometric not-linearity of the pendulum on the response of the system, showing that its not-linearity cannot be neglected in this class of problems. Finally, based on the results, a hybrid control approach is proposed. These studies show that this control strategy is more efficient than the passive control alone and that it does not require a large amount of energy.